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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)
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
Chemical structures
species with simple topological identity could also demonstrate complicated topological structures in a larger spatial scale. Topological structures, along
Topological_polymers
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
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
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
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
Duality for locally compact abelian groups
main directions: for commutative topological groups that are not locally compact, and for noncommutative topological groups. The theories in these two
Pontryagin_duality
Hypothetical compact star
Stellar black hole Compact star Exotic star Boson star Electroweak star Preon star Strange star Quark star Non-topological soliton § Soliton-stars Gravitational
Q_star
Infinitely detailed mathematical structure
curve map is not a homeomorphism, so it does not preserve topological dimension. The topological dimension and Hausdorff dimension of the image of the Hilbert
Fractal
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
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
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)
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
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
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
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
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)
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
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
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
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
Generalized 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
is a topology on X. Topological sum See Coproduct topology. Topologically complete Completely metrizable spaces (i. e. topological spaces homeomorphic
Glossary_of_general_topology
Mathematical concept
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
Relative location of objects in space
plays a central role. Commonly used types of spatial relations are: topological, directional and distance relations. The DE-9IM model expresses important
Spatial_relation
Topological space of dimension zero
In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several
Zero-dimensional_space
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
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
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
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
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
Contraction of an astronomical object due to the influence of its gravity
of the star, at which point the collapse gradually comes to a halt as the outward thermal pressure balances the gravitational forces. The star then exists
Gravitational_collapse
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
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
partial order Star product Symmetric closure Transitive closure Topology & Orders Alexandrov topology & Specialization preorder Ordered topological vector space
Absolutely and completely monotonic functions and sequences
Absolutely_and_completely_monotonic_functions_and_sequences
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
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)
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
Subset of incomparable elements
partial order Star product Symmetric closure Transitive closure Topology & Orders Alexandrov topology & Specialization preorder Ordered topological vector space
Antichain
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
Polyhedron made of congruent kites arranged radially
its 2n faces are kites (sometimes also called deltoids). They are topologically related to the scalenohedra, which are half-symmetry variants with irregular
Trapezohedron
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)
chemically interesting molecular graphs from simpler component graphs. Topological indices are numerical graph invariants used to predict physico-chemical
Corona_product
Category used in algebraic topology
category used in algebraic topology as an alternative to the category of topological spaces, Top, as the latter lacks some properties that are common in practice
Category of compactly generated weak Hausdorff spaces
Category_of_compactly_generated_weak_Hausdorff_spaces
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
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
On chains and antichains in partial orders
partial order Star product Symmetric closure Transitive closure Topology & Orders Alexandrov topology & Specialization preorder Ordered topological vector space
Dilworth's_theorem
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
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
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
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
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
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)
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
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
Standard example in game theory
Strategic interaction Strategic move Strategy Subgame Succinct game Topological game Tragedy of the commons Uncorrelated asymmetry Win–win game Zero-sum
Prisoner's_dilemma
face-transitive star dipyramids containing star polygon arrangement of edges. It has 10 intersecting isosceles triangle faces. It is topologically identical
Pentagrammic_prism
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)
Adroja, X. Yan, A. Prokofiev, Q. Si & S. Paschen (2026). "Emergent topological semimetal from quantum criticality". Nature Physics. 22 (2). Springer
2026_in_science
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
Pairing where no unchosen pair prefers each other over their choice
Strategic interaction Strategic move Strategy Subgame Succinct game Topological game Tragedy of the commons Uncorrelated asymmetry Win–win game Zero-sum
Stable_matching_problem
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
Topics referred to by the same term
hypothetical topological feature of spacetime. Wormhole may also refer to: Bajoran wormhole, a wormhole located near the planet Bajor in the fictional Star Trek
Wormhole_(disambiguation)
2025 multimodal model by OpenAI
model made him "feel useless", and posted an uncommented image of the Death Star on X a day before GPT-5 was unveiled. List of large language models "GPT-5
GPT-5
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
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)
Paper-and-pencil game for two players
versions under the names of Celebrity Squares, Personality Squares and All Star Squares. In Tic-Tac-Dough, players put symbols up on the board by answering
Tic-tac-toe
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
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
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
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
Branch of mathematics
in many areas of geometry. For instance, planes can be studied as a topological surface without reference to distances or angles; it can be studied as
Geometry
Logical paradox in decision-making theory
Strategic interaction Strategic move Strategy Subgame Succinct game Topological game Tragedy of the commons Uncorrelated asymmetry Win–win game Zero-sum
Paradox_of_tolerance
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
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
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
Subset of real numbers that are greater than zero
line and, thus, has the structure of a multiplicative topological group or of an additive topological semigroup. For a given positive real number x , {\displaystyle
Positive_real_numbers
Hilbert–Smith conjecture: if a locally compact topological group has a continuous, faithful group action on a topological manifold, then the group must be a Lie
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
functional analysis and order theory, an ordered topological vector space, also called an ordered TVS, is a topological vector space (TVS) X that has a partial
Ordered topological vector space
Ordered_topological_vector_space
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
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
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
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
Lebesgue covering dimension (dimension theory) Metrization theorems (topological spaces) Nagata–Smirnov metrization theorem(general topology) Netto's
List_of_theorems
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
Number of windings of a polytope around its center of symmetry
genus is g, its density is 1−g. χ = V − E + F = 2D = 2(1−g). Density of topological sphere polyhedron is one, like a cube. v=8, e=12, f=6. Density of a genus
Density_(polytope)
Algebraic object with an ordered structure
guarantee that the operations + and × are continuous, so that F is a topological field. The Harrison topology is a topology on the set of orderings XF
Ordered_field
Overuse of a shared resource
Strategic interaction Strategic move Strategy Subgame Succinct game Topological game Tragedy of the commons Uncorrelated asymmetry Win–win game Zero-sum
Tragedy_of_the_commons
specifically in functional analysis and order theory, a topological vector lattice is a Hausdorff topological vector space (TVS) X {\displaystyle X} that has
Topological_vector_lattice
Prime knot named for John Horton Conway
and showed that the knot is not a smoothly slice knot, though it is topologically slice (the Kinoshita–Terasaka knot is both). Weisstein, Eric W. "Conway's
Conway_knot
Russia United States "for topological quantum computation, in which quantum information is encoded and protected using topological properties of many-body
List of Clarivate Citation laureates in Physics
List_of_Clarivate_Citation_laureates_in_Physics
Mathematical concept regarding posets in (partial) order theory
partial order Star product Symmetric closure Transitive closure Topology & Orders Alexandrov topology & Specialization preorder Ordered topological vector space
Linked_set
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
Russian mathematician
Sciences. He is a painter and illustrator of original artworks inspired by topological objects and structures. Fomenko is also widely known as a conspiracy
Anatoly_Fomenko
Mathematical transform that expresses a function of time as a function of frequency
duality map defined above. Given an abelian locally compact Hausdorff topological group G, as before we consider the space L1(G), defined using a Haar
Fourier_transform
Set theory concept
partial order Star product Symmetric closure Transitive closure Topology & Orders Alexandrov topology & Specialization preorder Ordered topological vector space
Club_set
Mathematics book
§3.10 Karl Reinhardt 4 The topology of tilings §4.1 Homeomorphism (topological equivalence), combinatorial equivalence, isotopy, Metamorphosis III,
Tilings_and_patterns
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TOPOLOGICAL STAR
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TOPOLOGICAL STAR
TOPOLOGICAL STAR
TOPOLOGICAL STAR
TOPOLOGICAL STAR
TOPOLOGICAL STAR
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