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In algebraic geometry, the h topology is a Grothendieck topology introduced by Vladimir Voevodsky to study the homology of schemes. It combines several
H_topology
Branch of mathematics
Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric
Topology
variety of topologies. Studying space of linear maps and these topologies can give insight into the spaces themselves. The article operator topologies discusses
Topologies on spaces of linear maps
Topologies_on_spaces_of_linear_maps
Electronic filter circuits defined by component connection
Electronic filter topology defines electronic filter circuits without taking note of the values of the components used but only the manner in which those
Electronic_filter_topology
Branch of mathematics
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants
Algebraic_topology
scheme is a v-covering. See h-topology, relation to the v-topology Bhatt & Mathew (2018) have introduced the arc-topology, which is similar in its definition
V-topology
Mathematical concept
In mathematics, weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators,
Weak_topology
alterations h topology Coverings are universal topological epimorphisms. Also, h = rh + fppf. v-topology (also called universally subtrusive topology): coverings
List of topologies on the category of schemes
List_of_topologies_on_the_category_of_schemes
Topologies on operators on a Hilbert space
norm topology.) The σ-weak topology or ultraweak topology or weak-* operator topology or weak-* topology or weak topology or σ(B(H), B(H)*) topology is
Operator_topologies
Structure in algebraic geometry
algebraic geometry, the Nisnevich topology, sometimes called the completely decomposed topology, is a Grothendieck topology on the category of schemes which
Nisnevich_topology
areas of topology, the focus here is on general topology. The following definitions are also fundamental to algebraic topology, differential topology and geometric
Glossary_of_general_topology
mathematics, the ultraweak topology, also called the weak-* topology, or weak-* operator topology or σ-weak topology, is a topology on B(H), the space of bounded
Ultraweak_topology
Topology made of cocountable subsets
Symbolically, the topology is typically written as T = { H ⊆ X : H = ∅ or X ∖ H is countable } . {\displaystyle {\mathcal {T}}=\{H\subseteq X:H=\varnothing
Cocountable_topology
In chemistry, topology (also known as chemical topology or molecular topology) provides a way of describing and predicting the molecular structure within
Topology_(chemistry)
American mathematician
R. H. Bing (October 20, 1914 – April 28, 1986) was an American mathematician who worked mainly in the areas of geometric topology and continuum theory
R._H._Bing
Locally convex topology on function spaces
strong operator topology, often abbreviated SOT, is the locally convex topology on the set of bounded operators on a Hilbert space H induced by the seminorms
Strong_operator_topology
List of concrete topologies and topological spaces
The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics.
List_of_topologies
Mathematical space with a notion of closeness
elements are called points, along with an additional structure called a topology, which can be defined as a set of neighbourhoods for each point that satisfy
Topological_space
Branch of topology
general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It
General_topology
Mathematical method for optimizing material layout under given conditions
Topology optimization is a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions
Topology_optimization
of open subsets. This is again a base for a topology on CL(X) called the Fell topology or the H-topology. Note, though, that the canonical map i : x ↦
Hypertopology
Application of set theory concept
filters to topology. Filters were introduced by Henri Cartan in 1937 as an alternative to the related notion of a net developed in 1922 by E. H. Moore and
Filters_in_topology
Electronic filter topology
The Sallen–Key topology is an electronic filter topology used to implement second-order active filters that is particularly valued for its simplicity
Sallen–Key_topology
Topology where the only open sets are the empty set and the entire space
In topology, a topological space with the trivial topology is one where the only open sets are the empty set and the entire space. Such spaces are commonly
Trivial_topology
Representation of mathematical space
of triangulations established a new branch in topology, namely piecewise linear topology (or PL topology). Its main purpose is to study the topological
Triangulation_(topology)
Graph topology applied to electrical and communications circuits, or biomolecules
Hi-C. Circuit topology categorizes the topological arrangement of these physical contacts, that are referred to as hard contacts (or h-contacts). Furthermore
Circuit_topology
Branch of mathematics studying (smooth) functions of manifolds
geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another. Geometric topology as an area
Geometric_topology
Mathematical discipline
In mathematics, categorical topology is an approach to topology (theory of spaces) through the concepts and methods in category theory, a branch of mathematics
Categorical_topology
Type of topology
the compact-open topology is a topology defined on the set of continuous maps between two topological spaces. The compact-open topology is one of the commonly
Compact-open_topology
Weak topology on function spaces
weak operator topology, often abbreviated WOT, is the weakest topology on the set of bounded operators on a Hilbert space H {\displaystyle H} , such that
Weak_operator_topology
Mathematical structure
In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C {\displaystyle {\mathcal {C}}} that makes the objects
Grothendieck_topology
Mathematical subject
In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example
Combinatorial_topology
Study of quantum mechanics through low-dimensional topology
Kauffman, Louis H.; Baadhio, Randy A. (1993). Quantum Topology. River Edge, NJ: World Scientific. ISBN 981-02-1544-4. Quantum Topology, a journal published
Quantum_topology
Continuous, position-preserving mapping from a topological space into a subspace
In topology, a retraction is a continuous mapping from a topological space into a subspace that preserves the position of all points in that subspace.
Retraction_(topology)
Topological space that is homeomorphic to a metric space
In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space. That is, a topological
Metrizable_space
complete upper semilattice, the Lawson topology on P is always a complete T1 topology. Formal ball G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M.
Lawson_topology
Nonempty compact connected metric space
In the mathematical field of point-set topology, a continuum (plural: "continua") is a nonempty compact connected metric space, or, less frequently, a
Continuum_(topology)
Topological space construction
In topology and related areas of mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed
Quotient_space_(topology)
In topology, a branch of mathematics, a collapse reduces a simplicial complex (or more generally, a CW complex) to a homotopy-equivalent subcomplex. Collapses
Collapse_(topology)
Vector space with a notion of nearness
scalar multiplication) are also continuous functions. Such a topology is called a vector topology and every topological vector space has a uniform topological
Topological_vector_space
Transformation of a topological space
In topology, especially algebraic topology, the cone of a topological space X {\displaystyle X} is intuitively obtained by stretching X into a cylinder
Cone_(topology)
Local and global geometry of the universe
the shape of the universe refers to both its local geometry and cosmic topology. Local geometry is defined primarily by its curvature, general relativity
Shape_of_the_universe
Dual pair of vector spaces
a range of locally convex topologies. Such topologies are called polar topologies. The weak topology is the weakest topology of this range. Throughout
Dual_system
Topology on a partially ordered set
In mathematics, the upper topology on a partially ordered set X is the coarsest topology in which the closure of a singleton { a } {\displaystyle \{a\}}
Upper_topology
All points and limit points in a subset of a topological space
In topology, the closure of a subset S of points in a topological space consists of all points in S together with all limit points of S. The closure of
Closure_(topology)
Topological Object
the geometric topology is a topology one can put on the set H of hyperbolic 3-manifolds of finite volume. Convergence in this topology is a crucial ingredient
Geometric_topology_(object)
Type of topological space
complexes and has particular significance for algebraic topology. It was initially introduced by J. H. C. Whitehead to meet the needs of homotopy theory.
CW_complex
Computable topology is a discipline in mathematics that studies the topological and algebraic structure of computation. Computable topology is not to be
Computable_topology
Topological space
Knaster (1893–1980) in continuum theory", Handbook of the history of general topology, Vol. 1, Dordrecht: Kluwer Acad. Publ., pp. 63–78, MR 1617581. Borsuk,
Dendroid_(topology)
Mathematical function with no sudden changes
most general continuous functions, and their definition is the basis of topology. A stronger form of continuity is uniform continuity. In order theory,
Continuous_function
spanning abstract algebra, algebraic topology and operator theory. Type theory Contents: Top A B C D E F G H I J K L M N O P Q R S T U V W X Y Z See
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
density topology on the real numbers is a topology on the real line that is different (strictly finer), but in some ways analogous, to the usual topology. It
Density_topology
ultrastrong topology, or σ-strong topology, or strongest topology on the set B(H) of bounded operators on a Hilbert space is the topology defined by the
Ultrastrong_topology
Branch of topology
In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions
Low-dimensional_topology
British mathematician (1904–1960)
contributions in differential topology, particularly on triangulations and their associated smooth structures. Whitehead, J. H. C. (October 1940). "On C1-Complexes"
J._H._C._Whitehead
Continuous function whose domain is a closed unit interval
into X . {\displaystyle X.} Paths play an important role in the fields of topology and mathematical analysis. For example, a topological space for which there
Path_(topology)
Operation in topology
In topology, a field of mathematics, the join of two topological spaces A {\displaystyle A} and B {\displaystyle B} , often denoted by A ∗ B {\displaystyle
Join_(topology)
Subfield of mathematical topology
Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational
Computational_topology
Branch of topology
String topology, a branch of mathematics, is the study of algebraic structures on the homology of free loop spaces. The field was started by Moira Chas
String_topology
Two-dimensional manifold
In topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional solid figures; for example, the sphere
Surface_(topology)
Dual space topology of uniform convergence on some sub-collection of bounded subsets
related areas of mathematics a polar topology, topology of G {\displaystyle {\mathcal {G}}} -convergence or topology of uniform convergence on the sets
Polar_topology
Topological space
printable 3D model of Bing's house at Thingverse Bing, R. H., Some Aspects of the Topology of 3-Manifolds Related to the Poincaré Conjecture, Lectures
House_with_two_rooms
the smallest topology which refines the euclidean topology, and contains Q ∩ [ 0 , 1 ] {\displaystyle Q\cap [0,1]} as an open set is H-closed but not
H-closed_space
Type of spatial relationship
Geospatial topology is the study and application of qualitative spatial relationships between geographic features, or between representations of such features
Geospatial_topology
Integer invariant of certain classes of topological manifolds
In the field of topology, the signature is an integer invariant which is defined for an oriented manifold M of dimension divisible by four. This invariant
Signature_(topology)
Mathematical concept
point-weak topology. In terms of convergence of nets, this topology is defined by πi → π; if and only if ⟨ π i ( x ) ξ ∣ η ⟩ → ⟨ π ( x ) ξ ∣ η ⟩ ∀ ξ , η ∈ H n
Spectrum_of_a_C*-algebra
(old style), Gaelic football, rugby, hurling) are described as "H-shaped" H topology in electronic filter design Also see Balbis I-shape, the shape that
Glossary of shapes with metaphorical names
Glossary_of_shapes_with_metaphorical_names
Mathematics glossary
properties and concepts in algebraic topology in mathematics. See also: glossary of topology, list of algebraic topology topics, glossary of category theory
Glossary of algebraic topology
Glossary_of_algebraic_topology
Result on the topology of operators on an infinite-dimensional, complex Hilbert space
the topology of operators on an infinite-dimensional, complex Hilbert space H. It states that the space GL(H) of invertible bounded endomorphisms of H is
Kuiper's_theorem
Concept in topology
subject by Heinz Hopf (see J. R. Hubbuck. "A Short History of H-spaces", History of topology, 1999, pages 747–755). Spanier p.34; Switzer p.14 Hatcher p
H-space
Definition of continuity for functions between posets
The Scott-open subsets of a partially ordered set P form a topology on P, the Scott topology. A function between partially ordered sets is Scott-continuous
Scott_continuity
Analysis of datasets using techniques from topology
(TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information from datasets that are high-dimensional, incomplete
Topological_data_analysis
Theorem in geometric topology
In the mathematical field of geometric topology, the Poincaré conjecture (UK: /ˈpwæ̃kæreɪ/, US: /ˌpwæ̃kɑːˈreɪ/, French: [pwɛ̃kaʁe]) is a theorem about
Poincaré_conjecture
Topology on the space of semimartingales
In martingale theory, Émery topology is a topology on the space of semimartingales. The topology is used in financial mathematics. The class of stochastic
Émery_topology
and related areas of mathematics, the Mackey topology, named after George Mackey, is the finest topology for a topological vector space which still preserves
Mackey_topology
Inclusion of one mathematical structure in another, preserving properties of interest
{\displaystyle Y} , so that X ⊆ Y {\displaystyle X\subseteq Y} . In general topology, an embedding is a homeomorphism onto its image. More explicitly, an injective
Embedding
Continuous deformation between two continuous functions
In topology, two continuous functions from one topological space to another are called homotopic (from Ancient Greek: ὁμός homós 'same, similar' and τόπος
Homotopy
Form taken by the network of interconnections of a circuit
The circuit topology of an electronic circuit is the form taken by the network of interconnections of the circuit components. Different specific values
Circuit_topology_(electrical)
Generalization of a sequence of points
In mathematics, more specifically in general topology and related branches, a net or Moore–Smith sequence is a function whose domain is a directed set
Net_(mathematics)
Type of mathematical space
In mathematics, especially general topology and mathematical analysis, compactness is a property of a space that makes it behave in many ways like a finite
Compact_space
Topological space with a notion of uniform properties
In the mathematical field of topology, a uniform space is a set with additional structure that is used to define uniform properties, such as completeness
Uniform_space
Hilbert space H, containing the identity operator, and closed under taking adjoints. Then the closures of M in the weak operator topology and the strong
Von Neumann bicommutant theorem
Von_Neumann_bicommutant_theorem
Mathematical concept
doi:10.1090/s0002-9904-1958-10168-8. ISSN 1088-9485. Kozlov, Dmitry (2008). Combinatorial Algebraic Topology. Berlin: Springer. ISBN 978-3-540-71961-8.
Shelling_(topology)
In topology, the split interval, or double arrow space, is a topological space that results from splitting each point in a closed interval into two adjacent
Split_interval
Concept in topology
In mathematics, especially in algebraic topology, the mapping space between two spaces is the space of all the (continuous) maps between them. Viewing
Mapping_space
Network topology for parallel computers
a high-speed network. This form of multistage interconnection network topology can be used to connect different nodes in a multiprocessor system. The
Butterfly_network
In algebraic topology, the nth symmetric product of a topological space consists of the unordered n-tuples of its elements. If one fixes a basepoint, there
Symmetric_product_(topology)
JSON subset for geospatial data
of GeoJSON is TopoJSON, an extension of GeoJSON that encodes geospatial topology and that typically provides smaller file sizes. The GeoJSON format working
GeoJSON
Concept in topology
In the mathematical subject of topology, an ambient isotopy, also called an h-isotopy, is a kind of continuous distortion of an ambient space, for example
Ambient_isotopy
Theorem in symplectic topology
In the mathematical field of symplectic topology, Gromov's compactness theorem states that a sequence of pseudoholomorphic curves in an almost complex
Gromov's compactness theorem (topology)
Gromov's_compactness_theorem_(topology)
Scottish-American mathematician
first steps. NY: W. H. Benjamin. 1968. ISBN 9780805394856. reprint. Dover. 2006. Algebraic topology: homology and cohomology. NY: W. H. Benjamin. 1970. reprint
Andrew_H._Wallace
an adjunction space (or attaching space) is a common construction in topology where one topological space is attached or "glued" onto another. Specifically
Adjunction_space
Topological group that is in a certain sense assembled from a system of finite groups
{Z} } for n ≥ m . {\displaystyle n\geq m.} The topology on this profinite group is the same as the topology arising from the p {\displaystyle p} -adic valuation
Profinite_group
Research field in deep learning
mathematical foundations of TDL are algebraic topology, differential topology, and geometric topology. Therefore, TDL can be generalized for data on
Topological_deep_learning
Concept in topology
geometric topology and differential topology, an (n + 1)-dimensional cobordism W between n-dimensional manifolds M and N is an h-cobordism (the h stands
H-cobordism
Algebraic topology uses abstract algebra to study topological spaces
This is a list of algebraic topology topics. Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological
List of algebraic topology topics
List_of_algebraic_topology_topics
Mathematical space
3-manifolds. It shows that nontrivial limits exist in H. Troels Jorgensen's study of the geometric topology further shows that all nontrivial limits arise by
3-manifold
Group theory theorem
states that if H is a closed subgroup of a Lie group G, then H is an embedded Lie group with the smooth structure (and hence the group topology) agreeing with
Closed-subgroup_theorem
Characterizes when a topological space is metrizable
In topology, the Bing metrization theorem, named after R. H. Bing, characterizes when a topological space is metrizable. The theorem states that a topological
Bing_metrization_theorem
This is a list of geometric topology topics. Knot (mathematics) Link (knot theory) Wild knots Examples of knots (and links) Unknot Trefoil knot Figure-eight
List of geometric topology topics
List_of_geometric_topology_topics
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H TOPOLOGY
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H TOPOLOGY
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