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Hypothetical horizonless compact object in general relativity
In physics, a topological star (also called a topological soliton in this context) is a smooth, horizonless solution of the five-dimensional Einstein–Maxwell
Topological_star
State of matter with insulating bulk but conductive boundary
material. But in a topological insulator, these bands are, in an informal sense, "twisted", relative to a trivial insulator. The topological insulator cannot
Topological_insulator
Operation in topology
two topological spaces A {\displaystyle A} and B {\displaystyle B} , often denoted by A ∗ B {\displaystyle A\ast B} or A ⋆ B {\displaystyle A\star B}
Join_(topology)
Analysis of datasets using techniques from topology
In applied mathematics, topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information
Topological_data_analysis
Type of mathematical set
simplicial complex. Topological spaces do not necessarily admit a triangulation and if they do, it is never unique. Topological manifolds of dimension
Simplicial_complex
Special class of solitons
quantum field theory, a non-topological soliton (NTS) is a soliton field configuration possessing, contrary to a topological one, a conserved Noether charge
Non-topological_soliton
Space with topology generated by convex sets
of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize
Locally convex topological vector space
Locally_convex_topological_vector_space
Duality for locally compact abelian groups
considerations. A topological group is a locally compact group if the underlying topological space is locally compact and Hausdorff; a topological group is abelian
Pontryagin_duality
Certain topology in mathematics
to accept a proper class as a topological space, then we may similarly view the class of all ordinals as a topological space with the order topology.
Order_topology
Chemical structures
species with simple topological identity could also demonstrate complicated topological structures in a larger spatial scale. Topological structures, along
Topological_polymers
Can be continuously shrunk to a point
In mathematics, a topological space X is contractible if the identity map on X is null-homotopic, i.e. if it is homotopic to some constant map. Intuitively
Contractible_space
Well-quasi-ordering of finite trees
partial order Star product Symmetric closure Transitive closure Topology & Orders Alexandrov topology & Specialization preorder Ordered topological vector space
Kruskal's_tree_theorem
Subsets whose union equals the whole set
star refinement.[citation needed] The language of covers is often used to define several topological properties related to compactness. A topological
Cover_(topology)
Mathematical term
topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance on a Hilbert
Weak_topology
Transformation of a topological space
That is, the topological cone agrees with the geometric cone for compact spaces when the latter is defined. However, the topological cone construction
Cone_(topology)
Topological space that locally resembles Euclidean space
structure, or that only its topological properties are being considered. Formally, a topological manifold is a topological space locally homeomorphic to
Manifold
Topological space which is a generalization of certain compact spaces
In mathematics, a paracompact space is a topological space in which every open cover has an open refinement that is locally finite. These spaces were
Paracompact_space
is a topology on X. Topological sum See Coproduct topology. Topologically complete Completely metrizable spaces (i. e. topological spaces homeomorphic
Glossary_of_general_topology
Order-preserving mathematical function
connected subspace of X . {\displaystyle X.} In functional analysis on a topological vector space X {\displaystyle X} , a (possibly non-linear) operator T
Monotonic_function
Intelligence of machines
results in the International Math Olympiad of 2025. Topological deep learning integrates various topological approaches. According to Nicolas Firzli, director
Artificial_intelligence
Exterior algebraic map taking tensors from p forms to n-p forms
ζ {\displaystyle {\star }\zeta } has zero boundary values. (The proper definition of the above requires specifying a topological vector space that is
Hodge_star_operator
Property of point sets in Euclidean spaces
set Radial set – Topological set Star polygon – Regular non-convex polygon Symmetric set – Property of group subsets (mathematics) Star-shaped preferences
Star_domain
Natural satellite orbiting Earth
of the lunar highlands on the far side are also not well understood. Topological measurements show the crust on the near side to be thinner than on the
Moon
Construction in order theory
In mathematics, the star product is a method of combining graded posets with unique minimal and maximal elements, preserving the property that the posets
Star_product
Mathematical group of the homotopy classes of loops in a topological space
the topological space. The fundamental group is the first and simplest homotopy group. The fundamental group is a homotopy invariant—topological spaces
Fundamental_group
faces/vertex and up, and in increasing sides per face. This ordering allows topological similarities to be shown. There are infinitely many prisms and antiprisms
List_of_uniform_polyhedra
Flat-sided three-dimensional shape
notions form the basis of topological definitions of polyhedra, as subdivisions of a topological manifold into topological disks (the faces) whose pairwise
Polyhedron
Mathematical result in differential geometry
dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data). It includes many other theorems, such as
Atiyah–Singer_index_theorem
Topological space with a notion of uniform properties
metrizable. Similar to continuous functions between topological spaces, which preserve topological properties, are the uniformly continuous functions between
Uniform_space
Basilica under construction since 1882 in Barcelona, Spain
R.; Dunlop, G. M.; Maher, A. (2001). Drawing Together Euclidean and Topological Threads (PDF). The 13th Annual Colloquium of the Spatial Information
Sagrada_Família
American physicist (born 1963)
Lorentz Medal, again for work on topological insulators. Brumfiel, Geoff (2010-07-01). "Topological insulators: Star material". Nature News. 466 (7304):
Charles_L._Kane
Type of topology in mathematics
view of category theory, let Top denote the category of topological spaces consisting of topological spaces with continuous maps as morphisms. Let Alex denote
Alexandrov_topology
Polyhedron made of congruent kites arranged radially
are kites (sometimes also called trapezoids, or deltoids). They are topologically related to the scalenohedra, which are half-symmetry variants with irregular
Trapezohedron
Rule in mathematics
connections between selection principles and topological games. Let X {\displaystyle X} be a topological space. The Menger game G fin ( O , O ) {\displaystyle
Selection_principle
Topological complex vector space
mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties
C*-algebra
Bangladeshi physicist (born 1971)
new control knob for the quantum topological world". Physics World. 13 September 2018. ""How X-rays Pushed Topological Matter Research Over the Top" by
M._Zahid_Hasan
Representation of mathematical space
In mathematics, triangulation describes the replacement of topological spaces with simplicial complexes by the choice of an appropriate homeomorphism
Triangulation_(topology)
Generalized sphere of dimension n (mathematics)
{\displaystyle n} -sphere is the topological join of n + 1 {\displaystyle n+1} pairs of isolated points. Intuitively, the topological join of two pairs is generated
N-sphere
Concept in number theory
adele ring, often denoted A K {\displaystyle \mathbb {A} _{K}} , is a topological ring built from the completions K v {\displaystyle K_{v}} of K {\displaystyle
Adele_ring
Theorem about Diophantine approximations
monogenic closed subgroups of T (those with a single generator, in the topological sense), and sets of characters with kernel containing a given point.
Kronecker's_theorem
Adroja, X. Yan, A. Prokofiev, Q. Si & S. Paschen (2026). "Emergent topological semimetal from quantum criticality". Nature Physics. 22 (2). Springer
2026_in_science
Polyhedron with 6 faces
faces square, and three squares around each vertex. There are seven topologically distinct convex hexahedra, one of which exists in two mirror image forms
Hexahedron
admiral, vice admiral, admiral, (until about 2001, when all British five-star ranks were discontinued) admiral of the fleet, and the Lord High Admiral
Glossary of nautical terms (A–L)
Glossary_of_nautical_terms_(A–L)
Theoretical matter within neutron stars
core of the star. The pasta phases also have interesting topological properties characterized by homology groups. For a typical neutron star of 1.4 solar
Nuclear_pasta
Any of 4 regular star polyhedra
Dubrovin, Boris (1999). "Painlevé Transcendents in Two-Dimensional Topological Field Theory". In Conte, Robert (ed.). The Painlevé Property: One Century
Kepler–Poinsot_polyhedron
Hexagonal lattice made of carbon atoms
of opposite-sign mass is a hallmark of a topological phase and displays much the same physics as topological insulators. If the mass in graphene can be
Graphene
Characterizes spherical triangles with fixed base and area
triangulations of the sphere or texture mapping any triangular mesh topologically equivalent to a sphere. The analog of Lexell's theorem in the Euclidean
Lexell's_theorem
Property of a mathematical space
uniquely defined dimension of every connected topological manifold can be calculated. A connected topological manifold is locally homeomorphic to Euclidean
Dimension
consistent in the overall pattern, like a solid. Topological semimetals: Weyl semimetal Dirac semimetal Topological superconductor Metallic and insulating states
List_of_states_of_matter
Extended physical object in string theory
objects are mathematical structures (such as sets, vector spaces, or topological spaces) and the morphisms are functions between these structures. One
Brane
Visual depiction of a partially ordered set
partial order Star product Symmetric closure Transitive closure Topology & Orders Alexandrov topology & Specialization preorder Ordered topological vector space
Hasse_diagram
2006 film by Tony Scott
million. It was bought by Jerry Bruckheimer who got Denzel Washington to star and Tony Scott to direct. Rossio later wrote that Scott was "Completely the
Déjà_Vu_(2006_film)
Concept in algebraic topology
can be applied to all topological spaces, and so singular homology is expressible as a functor from the category of topological spaces to the category
Singular_homology
chemically interesting molecular graphs from simpler component graphs. Topological indices are numerical graph invariants used to predict physico-chemical
Corona_product
1954–1955 fantasy novel by J. R. R. Tolkien
and mythology. Commentators have attempted to identify literary and topological antecedents for characters, places and events in Tolkien's writings;
The_Lord_of_the_Rings
Any of the five regular polyhedra
dodecahedron. Altogether this makes five possible Platonic solids. A purely topological proof can be made using only combinatorial information about the solids
Platonic_solid
Mathematics glossary
mapping originally called a mapping "sans éclatement" topological chiral homology topological fundamental group transfer transgression triangulation
Glossary of algebraic topology
Glossary_of_algebraic_topology
2025 British television series
actress. "Don't miss this 'tense' British thriller with 'The Night Manager' star and lead 'unlike any on TV'". Digital Spy. 1 August 2025. Retrieved 23 November
The_Iris_Affair
Symbolic depiction of spatial relationships
logical relationships between items, rather than geographic relationships. Topological in nature, only the connectivity is significant. The London Underground
Map
Property of operations
and interior functions of the power set of a topological space to itself are idempotent; the Kleene star and Kleene plus functions of the power set of
Idempotence
American mathematician and computer scientist
Herbrand Award 1994 Scientific career Thesis Separative Measures for Topological Spaces (1953) Doctoral advisor Anthony Perry Morse Doctoral students
Woody_Bledsoe
Construct in functional analysis
any topological vector space, the closure of a balanced set is balanced. The union of the origin { 0 } {\displaystyle \{0\}} and the topological interior
Balanced_set
Axioms for defining a topology
subsets. Characterizations of the category of topological spaces – Multiple equivalent ways to define a topological spacePages displaying short descriptions
Kuratowski_closure_axioms
English writer and philologist (1892–1973)
mythology. Commentators have attempted to identify many literary and topological antecedents for characters, places and events in Tolkien's writings.
J._R._R._Tolkien
American mathematician and billionaire (1938–2024)
3-manifolds. Later, mathematical physicist Albert Schwarz discovered early topological quantum field theory, an application of the Chern–Simons form. It is
Jim_Simons
Four-dimensional geometric object with flat sides
4-polytope is a polygon, and the three-dimensional analogue is a polyhedron. Topologically 4-polytopes are closely related to the uniform honeycombs, such as the
4-polytope
Type of topological solutions in non-linear sigma models
name a model of the nucleon by proposed in 1961 by Tony Skyrme. As a topological soliton in the pion field, it has the remarkable property of being able
Skyrmion
Branch of discrete mathematics
separate field of study. There remain many connections with geometric and topological combinatorics, which themselves can be viewed as outgrowths of the early
Combinatorics
Equations describing classical electromagnetism
metric, gαβ and the d'Alembert operator is defined as ◻ = ∇α∇α. The topological restriction is that the second real cohomology group of the space vanishes
Maxwell's_equations
Graph that encodes local operations in mathematics
kind of flip graphs is obtained by considering the triangulations of a topological surface: consider such a surface S {\displaystyle {\mathcal {S}}} , place
Flip_graph
21 March 2019. Retrieved 25 April 2020. Rommel, Jacob (29 May 2014). Topological Analysis of the Evolution of Public Transport Networks (PDF) (MSc). KTH
List_of_metro_systems
Mathematical idealization of the surface of a body
distinguish them when needed. A topological surface is a surface that is a manifold of dimension two (see § Topological surface). A differentiable surface
Surface_(mathematics)
Order whose elements are all comparable
partial order Star product Symmetric closure Transitive closure Topology & Orders Alexandrov topology & Specialization preorder Ordered topological vector space
Total_order
States of matter for water as a solid
In Front Of Nearby Star. ScienceDaily. Retrieved Jan. 3, 2010, from "Astronomers Detect Shadow of Water World in Front of Nearby Star". Archived from the
Phases_of_ice
Polyhedron associated with another by swapping vertices for faces
kinds most relevant to elementary polyhedra are polar reciprocity and topological or abstract duality. In Euclidean space, the dual of a polyhedron P {\displaystyle
Dual_polyhedron
Lowest possible energy of a quantum system or field
QCD vacuum Quantum fluctuation Quantum foam Scalar field Time crystal Topological order Unruh effect Vacuum energy Vacuum expectation value Vacuum state
Zero-point_energy
Akbarov, S.S. (2003). "Pontryagin duality in the theory of topological vector spaces and in topological algebra". Journal of Mathematical Sciences. 113 (2):
Smith_space
Algebraic structure with "nice" duality properties
interest has been renewed in Frobenius algebras due to connections to topological quantum field theory. A finite-dimensional, unital, associative algebra
Frobenius_algebra
Symmetric monoidal closed category equipped with a dualizing object
extensions to categories of topological vector spaces can be made *-autonomous. On the other hand, the category of topological vector spaces contains an
*-autonomous_category
Aspect of topological graph theory
In topological graph theory, the Petrie dual of an embedded graph (on a 2-manifold with all faces disks) is another embedded graph that has the Petrie
Petrie_dual
Ghrist (M.A. 1994, Ph.D. 1995) – mathematician known for his work on topological methods in applied mathematics; the Andrea Mitchell Penn Integrating
List of Cornell University alumni (natural sciences)
List_of_Cornell_University_alumni_(natural_sciences)
Solid with 2 parallel n-gonal bases connected by n parallelograms
for even-sided base polygons. These are topological tori, with Euler characteristic of zero. The topological polyhedral net can be cut from two rows of
Prism_(geometry)
Theory of gravitation as curved spacetime
of X-ray bursts for which the central compact object is either a neutron star or a black hole; cf. Remillard et al. 2006 for an overview, Narayan 2006
General_relativity
Generalised alphabetical order
the name of the lexicographical order (of bits) in a binary tree traversal Star product – a different way of combining partial orders Shortlex order Orders
Lexicographic_order
Arrangement of a communication network
industrial fieldbusses and computer networks. Network topology is the topological structure of a network and may be depicted physically or logically. It
Network_topology
Concept in game theory
Strategic interaction Strategic move Strategy Subgame Succinct game Topological game Tragedy of the commons Uncorrelated asymmetry Win–win game Zero-sum
Focal_point_(game_theory)
Type of artificial neural network
minimization Occam learning PAC learning Statistical learning VC theory Topological deep learning Journals and conferences AAAI CVPR ECCV ECML PKDD EMNLP
Feedforward_neural_network
Hypothetical type of nuclear reaction
Kaiser, David I.; Kaur, Jasleen (July 2009), "Scientific discovery and topological transitions in collaboration networks" (PDF), Journal of Informetrics
Cold_fusion
Linear map from a vector space to its field of scalars
called the dual space of V, or sometimes the algebraic dual space, when a topological dual space is also considered. It is often denoted Hom(V, k), or, when
Linear_form
February – Microsoft unveils Majorana 1, a quantum chip powered by its new topological core architecture that it hopes will enable quantum computers capable
2025_in_science
Equalities for combinations of sets
Munkres 2000, p. 21 Lee p.388 of Lee, John M. (2010). Introduction to Topological Manifolds, 2nd Ed. Lee Halmos 1960, p. 39 Lee Munkres 2000, p. 19 Durrett
List of set identities and relations
List_of_set_identities_and_relations
Continuous surjection satisfying a local triviality condition
was that for Seifert what is now called the base space (topological space) of a fiber (topological) space E was not part of the structure, but derived from
Fiber_bundle
Ingarden, Roman (1993). "Juliusz Schauder: Personal Reminiscences". Topological Methods in Nonlinear Analysis. 2 (1): 1–14. doi:10.12775/TMNA.1993.026
List_of_Jewish_mathematicians
Hungarian and American mathematician and physicist (1903–1957)
defining locally convex spaces and topological vector spaces for the first time. In addition several other topological properties he defined at the time
John_von_Neumann
Mechanism by which a celestial body generates a magnetic field
be also viewed as the phenomenon of the spontaneous breakdown of the topological supersymmetry of the associated stochastic differential equation related
Dynamo_theory
from imploding bubbles in a liquid when excited by sound? Topological order: Is topological order stable at non-zero temperature? Equivalently, is it
List of unsolved problems in physics
List_of_unsolved_problems_in_physics
Partition of a toroidal surface into polygons
polyhedron is a polyhedron which is also a toroid (a g-holed torus), having a topological genus (g) of 1 or greater. Notable examples include the Császár and Szilassi
Toroidal_polyhedron
Decision rule used for minimizing the possible loss for a worst-case scenario
Strategic interaction Strategic move Strategy Subgame Succinct game Topological game Tragedy of the commons Uncorrelated asymmetry Win–win game Zero-sum
Minimax
Situation where total gains match total losses
Strategic interaction Strategic move Strategy Subgame Succinct game Topological game Tragedy of the commons Uncorrelated asymmetry Win–win game Zero-sum
Zero-sum_game
Fluid which flows without losing kinetic energy
electron–lattice interaction, it is expected that nucleons in a neutron star at sufficiently high density and low temperature can also form Cooper pairs
Superfluidity
TOPOLOGICAL STAR
TOPOLOGICAL STAR
Surname or Lastname
English
English : patronymic from Stark.
Surname or Lastname
English
English : variant spelling of Starkey.
Surname or Lastname
English
English : patronymic from Stark.
Surname or Lastname
English
English : unexplained. Compare Starnes.
Surname or Lastname
English (Kent)
English (Kent) : apparently a nickname from Middle English sterten ‘to leap or jump’ + up. Reaney and Wilson note that startup was the original form of ‘upstart’ and also the name of a kind of rustic boot and believe these senses may have contributed to the surname, although neither is recorded beofe the 16th century.
Surname or Lastname
English
English : unexplained.Perhaps an Americanized spelling of Czech and Slovak Starý ‘old’ (see Stary).
Surname or Lastname
English
English : nickname from Middle English sterre, starre ‘star’. The word was also used in a transferred sense of a patch of white hair on the forehead of a horse, and so perhaps the name denoted someone with a streak of white hair. It is possibly also a habitational name, for someone who lived at a house distinguished by the sign of a star.Jewish (Ashkenazic) : variant of Star 1 and 3.
Surname or Lastname
English
English : altered form of Starling.
Surname or Lastname
English
English : variant of Starr 1.English : from the medieval nickname Starre (see Starr 1) + man ‘servant’, hence an occupational name for the servant of a man known as ‘Star’.
Surname or Lastname
English
English : habitational name from any of the various minor places, for example Start Point in Devon, named from Old English steort ‘tail’, in the transferred sense of a promontory or spur of a hill.
Surname or Lastname
English
English : from Middle English starling ‘starling’ (Old English stærling), probably a nickname for a raucous or voracious person.
Boy/Male
English
Star deer.
Surname or Lastname
English
English : from a diminutive of Stark 1.Altered spelling of German Starke, written thus to preserve the second syllable.
Surname or Lastname
English
English : unexplained. Perhaps a nickname for a stormy-tempered person. Compare Stark.
Girl/Female
English American
Star.
Girl/Female
English
Star.
Surname or Lastname
English
English : unexplained (Starns).
Surname or Lastname
English (mainly Leicestershire)
English (mainly Leicestershire) : habitational name from Starbeck in Harrogate, North Yorkshire.
Boy/Male
Shakespearean
A Midsummer Night's Dream' Starveling, a tailor, acts as Moonshine in the play within the play.
Surname or Lastname
English, German (Starkmann), and Jewish (Ashkenazic)
English, German (Starkmann), and Jewish (Ashkenazic) : elaborated form of Stark.
TOPOLOGICAL STAR
TOPOLOGICAL STAR
Girl/Female
British, English
Beautiful
Boy/Male
Indian
Feeling, Virtual
Girl/Female
African, Bengali, French, Gujarati, Hindu, Indian, Italian, Kannada, Latin, Malayalam, Sanskrit
Quiet and Frisky; Option; Happiness; Joy
Surname or Lastname
English
English : unexplained.Perhaps an Americanized spelling of Czech and Slovak Starý ‘old’ (see Stary).
Girl/Female
Latin American Greek Irish English Shakespearean
Pure, clear. Form of the Latin 'Katharina', from the Greek 'Aikaterina'. It was borne by a number...
Girl/Female
Indian, Marathi
Decent; Benevolent; Loud; Lucky
Boy/Male
Australian, Jamaican
A Bright Rock
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Rajasthani, Sanskrit, Sindhi, Tamil, Telugu, Traditional
Full Moon; Beauty; Softness
Girl/Female
Muslim
Good natured
Girl/Female
Muslim
Jasmine
TOPOLOGICAL STAR
TOPOLOGICAL STAR
TOPOLOGICAL STAR
TOPOLOGICAL STAR
TOPOLOGICAL STAR
a.
Of or pertaining to pomology.
a.
Alt. of Posological
a.
Theological.
v. i.
To introduce innovations in doctrine, esp. in theological doctrine.
v. t.
To use in a tropological sense, as a word; to make a trope of.
a.
Characterized by tropes; varied by tropes; tropical.
a.
Of or pertaining to nosology.
a.
Pertaining to posology.
a.
Of or pertaining to zoology, or the science of animals.
a.
Alt. of Tropological
a.
Of or pertaining to oology.
a.
Relating to a horologe, or to horology.
a.
Of or pertaining tootology.
a.
Of or pertaining to theology, or the science of God and of divine things; as, a theological treatise.
n.
A student in a theological seminary.
a.
Of or pertaining to orology.
adv.
In a zoological manner; according to the principles of zoology.
a.
Pertaining to doxology; giving praise to God.
a.
Of or pertaining to noology.
a.
Pertaining to homology; having a structural affinity proceeding from, or base upon, that kind of relation termed homology.