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Topological space
topology, a branch of mathematics, the loop space ΩX of a pointed topological space X is the space of (based) loops in X, i.e. continuous pointed maps from
Loop_space
Describes a periodicity in the homotopy groups of classical groups
describes the twofold loop space, Ω 2 B U {\displaystyle \Omega ^{2}BU} of BU. Here, Ω {\displaystyle \Omega } is the loop space functor, right adjoint
Bott_periodicity_theorem
homotopy (in a nice way), an infinite loop space machine produces a group completion of X together with infinite loop space structure. For example, one can
Infinite_loop_space_machine
Topological path whose initial point is equal to its terminal point
In mathematics, a loop in a topological space X is a continuous function f from the unit interval I = [0,1] to X such that f(0) = f(1). In other words
Loop_(topology)
On the loop space of a wedge of spheres
Peter Hilton (1955), states that the loop space of a wedge of spheres is homotopy-equivalent to a product of loop spaces of spheres. John Milnor (1972) showed
Hilton's_theorem
Mathematical group of the homotopy classes of loops in a topological space
fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space. It records information about
Fundamental_group
Theory of quantum gravity merging quantum mechanics and general relativity
of quantum space. Research has evolved in two directions: the more traditional canonical loop quantum gravity, and the newer covariant loop quantum gravity
Loop_quantum_gravity
Mathematical group of loops in a Lie group
For compact G, smooth loop groups are modeled on nuclear Fréchet spaces. The free loop group of G is LG itself. The based loop group is Ω G = { γ ∈ L
Loop_group
Concept in mathematics
{\displaystyle X} a loop in Y {\displaystyle Y} (an element of the loop space Ω Y {\displaystyle \Omega Y} ), and the trivial loop should be associated
Suspension_(topology)
𝐀∞-space. There are three consequences of this characterization of loop spaces. First, a loop space is an A∞-space. Second, a connected A∞-space X is
A∞-operad
Topological construction defined up to homotopy
and }}\gamma (1)=x_{0}\right\}} which is the loop space Ω X {\displaystyle \Omega X} . See also: Path space fibration. Given a universal covering π : X
Homotopy_fiber
Proposed system for launching objects into orbit
launching humans for space tourism, space exploration and space colonization, and provides a relatively low 3g acceleration. Launch loops were described by
Launch_loop
Mathematical theory of topological spaces
used rational homotopy theory to show that the Betti numbers of the free loop space of X are unbounded. The theorem then follows from a 1969 result of Detlef
Rational_homotopy_theory
French-British singer
including: DJ Supreme, Kings of Rhythm, Loop Da Loop, and DJ Chrome. In 2002, Dresti changed his stage name to Space Cowboy and did a cover of Prince's song
Space_Cowboy_(musician)
Topological variant of the loop
distinguished point. Formally, let X {\displaystyle X} be a topological space. Then a free loop in X {\displaystyle X} is an equivalence class of continuous functions
Free_loop
Infinite loop space
they are En-spaces.) Conversely, any connected En-space X is an n-fold loop space on some other space (called BnX, the n-fold classifying space of X). The
E∞-operad
Topological space with only one nontrivial homotopy group
idea is sketched later as well. The loop space of an Eilenberg–MacLane space is again an Eilenberg–MacLane space: Ω K ( G , n ) ≅ K ( G , n − 1 ) {\displaystyle
Eilenberg–MacLane_space
Type of textile fastener
astronauts maneuver in and out of bulky space suits. However, this use reinforced the view among the populace that hook-and-loop was something with very limited
Velcro
Concept in topology
groups of an H-space. The fundamental group of an H-space is abelian. To see this, let X be an H-space with identity e and let f and g be loops at e. Define
H-space
Generalization of associativity properties
in algebraic topology; they were introduced to characterize iterated loop spaces by J. Michael Boardman and Rainer M. Vogt in 1968 and by J. Peter May
Operad
Manifold modelled on Hilbert spaces
topology of the free loop space, especially in the field of string topology. We can do an analogous Sobolev construction for the loop space, making it a codimension-
Hilbert_manifold
How spheres of various dimensions can wrap around each other
homology groups of its repeated loop spaces. The Serre spectral sequence relates the homology of a space to that of its loop space, so can sometimes be used
Homotopy_groups_of_spheres
Mathematical construction used in homotopy theory
one wants to prove that a space is a loop space. The basic idea is that if G {\displaystyle G} is a group with classifying space B G {\displaystyle BG}
Simplicial_set
Symplectic topology tool
free loop space of a symplectic manifold with the symplectic action functional. For the (instanton) version for three-manifolds, it is the space of SU(2)-connections
Floer_homology
Branch of topology
homology of free loop spaces. The field was started by Moira Chas and Dennis Sullivan (1999). While the singular cohomology of a space has always a product
String_topology
Cohomology theory related to elliptic curves
differential operators on free loop spaces. In some sense it can be seen as an approximation to the K-theory of the free loop space. Chromatic homotopy theory
Elliptic_cohomology
theory, the homotopy groups of spheres, and conjectural index theories on loop spaces of manifolds. tmf was first constructed by Michael Hopkins and Haynes
Topological_modular_forms
Type of radio antenna consisting of a loop or coil
A loop antenna is a radio antenna consisting of a loop or coil of wire, tubing, or other electrical conductor, that for transmitting is usually fed by
Loop_antenna
Transforming a function in such a way that it only takes a single argument
turn the interval into a loop. The curried form then maps the space X {\displaystyle X} to the space of functions from loops into Z {\displaystyle Z}
Currying
American mathematician
on algebraic K-theory. His results include a proof that all infinite loop space machines are in some sense equivalent, and progress on the Quillen–Lichtenbaum
Robert_Wayne_Thomason
Process where information about current status is used to influence future status
as inputs as part of a chain of cause and effect that forms a circuit or loop. The system can then be said to feed back into itself. The notion of cause-and-effect
Feedback
Control flow construct for executing code repeatedly
programming, a loop is a control flow construct that allows code to be executed repeatedly, usually with minor alterations between repetitions. Loops can be used
Loop_(statement)
2004 single by Asian Kung-Fu Generation
"Loop & Loop" (ループ&ループ, Rūpu&Rūpu) is a song by the Japanese rock band Asian Kung-Fu Generation. It was the second single released from their second full-length
Loop_&_Loop
Concept in algebraic topology
& Wilkerson (1994), making precise earlier notions of a mod p finite loop space. A p-compact group has many Lie-like properties like maximal tori and
P-compact_group
the James reduced product J(X) has the same homotopy type as ΩΣX, the loop space of the suspension of X. The commutative analogue of the James reduced
James_reduced_product
Topics referred to by the same term
see path space fibration#Moore's path space. See also: loop space, the space of loops in a topological space This disambiguation page lists mathematics
Path_space
where Ω {\displaystyle \Omega } stands for a loop space and the (2) is localization of a topological space at the prime 2. This gives a spectral sequence
EHP_spectral_sequence
Assistive listening technology
the looped space which can be picked up by a telecoil-equipped hearing aid, a cochlear implant (CI) processor, or a specialized hand-held hearing loop receiver
Audio_induction_loop
Set of functions between two fixed sets
example is the compact-open topology, e.g. loop space. Also available is the product topology on the space of set theoretic functions (i.e. not necessarily
Function_space
) {\displaystyle (X,*)} ; thus it is the loop space of ( X , ∗ ) {\displaystyle (X,*)} . The free path space of X, that is, Map ( I , X ) = X I {\displaystyle
Path_space_fibration
Space which has no holes through it
group is trivial. A topological space X {\displaystyle X} is called simply connected if it is path-connected and any loop in X {\displaystyle X} defined
Simply_connected_space
Cohomology class
of loop spaces. A loop space ΩX has a multiplication Ω X × Ω X → Ω X {\displaystyle \Omega X\times \Omega X\to \Omega X} by composition of loops. Here
Highly structured ring spectrum
Highly_structured_ring_spectrum
Theorem
conjecture is a conjecture made by Brayton Gray in 1984 about maps between loop spaces of spheres. It was later proved by John Harper. Gray, Brayton (1984)
Gray's_conjecture
Type of group in mathematics
dimensions of the vector spaces over the two points, so π0(KO) = Z is the dimension. Using concrete descriptions of the loop spaces in Bott periodicity, one
Orthogonal_group
Former corporate headquarters of Apple Inc. in California, U.S.
The Apple Infinite Loop campus (also known as Apple Campus 1 and by its address, 1 Infinite Loop) is an office complex owned and occupied by Apple Inc
Apple_Infinite_Loop_campus
Loop transformation technique
as space–time tradeoff. The transformation can be undertaken manually by the programmer or by an optimizing compiler. On modern processors, loop unrolling
Loop_unrolling
Mathematics glossary
homotopy groups and homology groups. infinite loop space infinite loop space machine Infinite loop space machine. infinite mapping telescope intersection
Glossary of algebraic topology
Glossary_of_algebraic_topology
Mathematical set with some added structure
product space Kolmogorov space Lp-space Lens space Liouville space Locally finite space Loop space Lorentz space Mapping space Measure space Metric space Minkowski
Space_(mathematics)
Branch of engineering and mathematics
placement can be performed mathematically using a state space representation of the open-loop system and calculating a feedback matrix assigning poles
Control_theory
American theoretical physicist
conformal and exactly integrable field theories and string theory in loop space. In solid state physics, he is primarily concerned with highly correlated
Natan_Andrei
Algebraic theorem
}(\Omega X;\mathbb {Q} ),} where Ω X {\displaystyle \Omega X} denotes the loop space of X, compare with Theorem 21.5 from Félix, Halperin & Thomas (2001).
Milnor–Moore_theorem
Aspect of astrophysics history
special relativity) replaces the group of rotational symmetries of space. (Later, loop quantum gravity inherited this geometric interpretation of gravity
History of loop quantum gravity
History_of_loop_quantum_gravity
Continuous function whose domain is a closed unit interval
of a space X {\displaystyle X} is often denoted π 0 ( X ) . {\displaystyle \pi _{0}(X).} One can also define paths and loops in pointed spaces, which
Path_(topology)
English rock band
The Pop Group and Can tracks. Hampson's MySpace pages referred to friendly pressure to again re-release the Loop albums and these were eventually released
Loop_(band)
Mathematical concept
spaces of infinite dimension. In particular, this is the case of iterated loop spaces. The structure of a fractal object is reiterated in its magnifications
Infinity
Concept in math
category of spaces. For example, the suspension ΣX and the loop space ΩX are defined for a pointed space X and produce another pointed space. Also, the
Homotopy_category
Rail loop for turning vehicles
A balloon loop, turning loop, or reversing loop (North American Terminology) allows a rail vehicle or train to reverse direction without having to shunt
Balloon_loop
Roller coaster at Enchanted Kingdom, Santa Rosa, Laguna, Philippines
boomerang by the designers), then travels through a vertical loop. Upon exiting the loop, the train runs up a second spike, which is angled so that the
Space Shuttle (roller coaster)
Space_Shuttle_(roller_coaster)
2022 studio album by Loop
alternative rock band Loop. It was released in 2022 by Reactor Records and peaked at #89 in the UK Albums Chart. Sonancy was Loop's first album in 32 years
Sonancy
Theater in Chicago, Illinois
Nederlander Theatre is a theater located at 24 West Randolph Street in the Loop area of downtown Chicago, Illinois. It opened in 1926, named the Oriental
Nederlander_Theatre_(Chicago)
Branch of mathematics
CW complex, then so does its loop space Ω X {\displaystyle \Omega X} . Given a topological group G, the classifying space for principal G-bundles ("the"
Homotopy_theory
Possibility of a consistent definition of "clockwise" in a mathematical space
orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows
Orientability
2021 video game
Loop Hero is a 2021 roguelike video game developed by Russian studio Four Quarters and published by Devolver Digital for Linux, macOS, and Windows. It
Loop_Hero
Electronic control system
A phase-locked loop (PLL) is a control system that generates an output signal whose phase is fixed relative to the phase of an input signal. Keeping the
Phase-locked_loop
Spectral sequence in algebraic topology
the loop space. This is an example of a case where we can study the homology of a fibration by using the E∞ page (the homology of the total space) to
Serre_spectral_sequence
State highway loops in Texas are owned and maintained by the Texas Department of Transportation (TxDOT). Loop 300 was a proposed route in Snyder. It was
List of state highway loops in Texas (300–399)
List_of_state_highway_loops_in_Texas_(300–399)
Self-reproducing cellular automaton patterns
particular property of the loops' "pseudopodia", they are unable to reproduce into the space occupied by another loop. Thus, once a loop is surrounded, it is
Langton's_loops
American infrastructure and tunneling company
as a subsidiary of SpaceX in 2017, and was spun off as a separate corporation in 2018. The original Las Vegas Convention Center Loop (1.7 miles, three
The_Boring_Company
Mathematical product in topology
an abelian group, the Pontryagin product on an H-space, and the Pontryagin product on a loop space. In order to define the Pontryagin product we first
Pontryagin_product
Cloud of heated and ionized gas and dust in the constellation Cygnus
It constitutes the brightest parts of the visible portion of the Cygnus Loop, a supernova remnant, many portions of which have acquired their own individual
Veil_Nebula
Pathological embedding of the sphere in 3D space
three-dimensional space. Together with its inside, it is a topological 3-ball, the Alexander horned ball, and so is simply connected; i.e., every loop can be shrunk
Alexander_horned_sphere
American science fiction drama TV series
of light and space all do justice to Stålenhag's retrofuturistic vision". According to The Verge's Joshua Rivera, "Tales from the Loop is so pretty it
Tales_from_the_Loop
Void between celestial bodies
Outer space, or simply space, is the expanse that exists beyond Earth's atmosphere and between celestial bodies. It contains ultra-low levels of particle
Outer_space
In computer science, a loop variant is a mathematical function defined on the state space of a computer program whose value is monotonically decreased
Loop_variant
fiction Category:Time loop television series Category:Time loop television episodes Category:Video games about time loops Category:Time loop novels Matthew Jones;
List of films featuring time loops
List_of_films_featuring_time_loops
Community area in Chicago, Illinois
The Loop is Chicago's central business district and one of the 77 municipally-designated community areas of Chicago in Illinois, United States. Located
Chicago_Loop
Neighborhood in Chicago, Illinois, United States
South Loop is a Chicago neighborhood south of the Loop. The South Branch of the Chicago River flows through it. Chinatown is adjacent to the southwest
South_Loop
Canadian mathematician (born 1942)
University of Lille. His research deals with homotopy theory and homology of loop spaces with applications in geometry. He wrote a three-volume textbook on differential
Stephen_Halperin
Non-orientable surface with one edge
In mathematics, a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist
Möbius_strip
American mathematician (born 1974)
Amer. Math. Soc. 23 (2010), 909-966 David Ben-Zvi and David Nadler, Loop spaces and connections, Journal of Topology, Volume 5, Issue 2, June 2012, Pages
David_Ben-Zvi
preserves limits. The objects in the image have the structure of infinite loop spaces; whence, the notion is a generalization of the corresponding notion (stabilization
Stable_∞-category
Theoretical physicist and mathematician
Duisburg-Essen in 2005 with a thesis supervised by Robert Graham and titled From Loop Space Mechanics to Nonabelian Strings. Schreiber's research fields include the
Urs_Schreiber
Property in algebraic topology
of covering spaces. Roughly speaking, a topological space X satisfies the property if for each point x in X any sufficiently small loop going through
Semi-locally_simply_connected
2024 video game
to hack the Grand Reset, limiting its effect and saving the current loop's space-time. Grendel Shaddai, meanwhile, prevents Van's group from stopping
The Legend of Heroes: Trails Beyond the Horizon
The_Legend_of_Heroes:_Trails_Beyond_the_Horizon
Loops of magnetic tape to create patterns or sounds
In music, tape loops are loops of magnetic tape used to create repetitive, rhythmic musical patterns or dense layers of sound when played on a tape recorder
Tape_loop
Type of topology
{\displaystyle \Omega (X,x_{0})=\{f:I\to X\mid f(0)=f(1)=x_{0}\}} , the loop space of X {\displaystyle X} at x 0 {\displaystyle x_{0}} , E ( X , x 0 , x
Compact-open_topology
Process to determine relationships among statements
In computer science, loop dependence analysis is a process which can be used to find dependencies within iterations of a loop with the goal of determining
Loop_dependence_analysis
Finite, symmetry-reduced model of loop quantum gravity
effects of loop quantum gravity (LQG). In particular, quantum geometry creates a brand new repulsive force which is totally negligible at low space-time curvature
Loop_quantum_cosmology
Modular space station in low Earth orbit
The International Space Station (ISS) is a space station in low Earth orbit (LEO). It is the product of the International Space Station program and is
International_Space_Station
Concept in algebraic topology
paths. The fiber is denoted by Ω B {\displaystyle \Omega B} and is called loop space. The fibers p − 1 ( b ) {\displaystyle p^{-1}(b)} over b ∈ B {\displaystyle
Fibration
Topological space with a distinguished point
spaces to itself. This functor is left adjoint to the functor Ω {\displaystyle \Omega } taking a pointed space X {\displaystyle X} to its loop space Ω
Pointed_space
inclined loop, also known as an oblique loop, is a 360° loop that has been tilted at an angle. It is not entered vertically, like a vertical loop, or horizontally
List of roller coaster elements
List_of_roller_coaster_elements
Mathematical object
{\to n}{\operatorname {colim} {}}}\Omega ^{n}E_{n}} called the infinite loop space of the spectrum. For a CW complex X {\displaystyle X} Ω ∞ Σ ∞ X = colim
Spectrum_(topology)
Establishes the concept of stabilization of homotopy groups
isomorphism if k ≤ 2n and an epimorphism if k = 2n + 1. A basic result on loop spaces gives the relation π k ( Ω ( Σ X ) ) ≅ π k + 1 ( Σ X ) {\displaystyle
Freudenthal suspension theorem
Freudenthal_suspension_theorem
Jamaican musical artist
"Release: Richie Loop - Manimal". www.reggaeville.com. Retrieved 2024-08-26. infojamaica (2024-08-03). "JP Backhouse & Richie Loop – SpaceHall Vol. 1 -"
Richie_Loop
Gauge field loop operator
field theory, Wilson loops are gauge invariant operators arising from the parallel transport of gauge variables around closed loops. They encode all gauge
Wilson_loop
Algorithm trading more space for lower time
jumping back to the beginning of the loop at the end of each iteration. Algorithms that also make use of space–time tradeoffs include: Baby-step giant-step
Space–time_tradeoff
Amusement ride
different vehicles, including a Space Shuttle, a fighter jet, an Egyptian cargo ship, and a Looney Tunes ACME Rocket. The Looping Starship is manufactured either
Looping_Starship
2025. Williscroft, Robert G. (August 21, 2015). "The Space Elevator, Space Launch Loop, Space Fountain, and Mass Driver in Science Fiction". sribd.com
Space_elevators_in_fiction
Concept in geometric topology
structure of an abelian group since the space G / O {\displaystyle G/O} is a loop space and in fact an infinite loop space so the normal invariants are a zeroth
Normal_invariant
travel, tourism, insurance
LOOP SPACE
LOOP SPACE
Boy/Male
British, English
Barrel Maker
Girl/Female
Hindu
Look, Blessed with beauty, Shape, Beauty
Surname or Lastname
North German
North German : habitational name from any of several places called Loose or Loosey.North German : from a short form of Nikolaus, German form of Nicholas.Dutch : nickname from the adjective loos ‘cunning’, ‘artful’, ‘guileful’.English : variant spelling of Loose.
Girl/Female
Tamil
Look, Blessed with beauty, Shape, Beauty
Surname or Lastname
English (Somerset)
English (Somerset) : habitational name from Look in Puncknowle, Dorset, named in Old English with lūce ‘enclosure’.English : possibly a variant of Luck 3.Northern English and Scottish : from a vernacular pet form of Lucas.Dutch (van Look) : topographic name from look ‘enclosure’ or habitational name from a place named with this word.Thomas Look (b. c. 1622) was in Lynn, MA, by 1646. His son, also called Thomas (b. 1646), moved to Martha’s Vineyard about 1670.
Surname or Lastname
Dutch
Dutch : from a short form of the Germanic personal name Robrecht.Altered spelling of German Rupp.English : variant spelling of Roope.
Girl/Female
Arabic, Muslim
Look
Boy/Male
Arabic
The Biblical Lot is the English Language Equivalent
Boy/Male
Hindu, Indian, Rajasthani, Sindhi, Traditional
Look; Beauty; Appearance
Boy/Male
Indian, Sanskrit
Natural; Original; Innate; Simply; Loop
Boy/Male
Hindu, Indian
Look
Boy/Male
Bengali, Indian
Loop; Autumn
Male
French
French form of Latin Lupus, LOUP means "wolf."
Male
Dutch
, Jehovah's gift (or grace).
Boy/Male
Dutch, German, Hebrew
God will Multiply; God will Add
Boy/Male
Hindu
Flower
Surname or Lastname
English
English : possibly from the Old Norse personal name Tópi, Túpi, a short form of a personal name formed with þórr, name of the Norse god of thunder (see Thor) + a second element with initial b-, for example björn ‘bear’, ‘warrior’. On the other hand, the name is found mainly in Dorset and Devon, which are far from areas of Scandinavian settlement.
Surname or Lastname
English
English : metonymic occupational name for a cooper, from Middle English coupe ‘tub’, ‘container’ (see Cooper). In some cases the surname may have been derived from a pub or house sign.Dutch : from koop ‘purchase’, ‘bargain’, hence a nickname for a haggler or a metonymic occupational name for a merchant.
Boy/Male
Hebrew
God will multiply.
Girl/Female
Gujarati, Hindu, Indian
Look
LOOP SPACE
LOOP SPACE
LOOP SPACE
LOOP SPACE
LOOP SPACE
LOOP SPACE
LOOP SPACE
travel, tourism, insurance