Search for "Topological groups" in article titles:

1. Direct sum of topological groups: In mathematics, a topological group \displaystyle{ G }[/math] is called the topological direct sum of two subgroups \displaystyle{ H_1 }[/math] and \displaystyle{ H_2 }[/math] if the map \displaystyle{ \begin{align} H_1\times H_2 &\longrightarrow G \\ (h_1,h_2) &\longmapsto h_1 h_2 ... [100%] 2024-07-25 [Topological groups] [Topology]...

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1. Topological group: A set $ G $ on which two structures are given — a group structure and a topology, such that the group operations are continuous. Specifically, the mapping $ (a, b) \mapsto ab ^ {-1} $ from the direct product $ G \times G $ into $ G $ must ... (Mathematics) [100%] 2022-11-28
2. Topological group: A topological group is a topological space that is also a group such that the binary operation defined on the group is a continuous map, as is the operation of inversion. Every group G can be turned into a topological ... [100%] 2023-06-24 [Topology] [Algebra]...
3. Galois topological group: A Galois group endowed with the Krull topology; the filter base (i.e. a basis of the open neighbourhoods of the identity) of this topology consists of normal subgroups of finite index. (Mathematics) [81%] 2023-09-25
4. Local topological group: A topological group in which the group operations are defined only for elements sufficiently close to the identity. The introduction of local topological groups was inspired by the study of the local structure of topological groups (that is, their structure ... (Mathematics) [81%] 2023-10-22
5. Topological semi-group: A set equipped with both the algebraic structure of a semi-group and the structure of a topological Hausdorff space, such that the semi-group operation is continuous in the given topology. Any semi-group is a topological semi-group ... (Mathematics) [81%] 2023-07-18
6. Topologika: Topologika Software Ltd was an independent United Kingdom publisher of educational software. Established in Stilton, Cambridgeshire in 1983, the company spent most of its life in Penryn, Cornwall before moving to Brighton, Sussex. (Company) [72%] 2023-11-10 [Educational software companies]
7. Topolovica: Cette page d’homonymie répertorie différentes localités partageant un même nom. Topolovica est un toponyme qui peut désigner. [72%] 2024-05-05
8. Topological degeneracy: In quantum many-body physics, topological degeneracy is a phenomenon in which the ground state of a gapped many-body Hamiltonian becomes degenerate in the limit of large system size such that the degeneracy cannot be lifted by any local ... (Physics) [64%] 2023-04-16 [Quantum phases] [Condensed matter physics]...
9. Topological structures: General topology (also called set-theoretic topology or analytic topology, cf. Topology, general) tries to explain such concepts as convergence and continuity known from classical analysis in a general setting. (Mathematics) [64%] 2023-10-17
10. Topological monoid: In topology, a branch of mathematics, a topological monoid is a monoid object in the category of topological spaces. In other words, it is a monoid with a topology with respect to which the monoid's binary operation is continuous. (Concept in mathematics) [64%] 2022-08-25 [Topological spaces] [Algebraic topology]...
11. Topological dynamics: Topological dynamics is the study of asymptotic or long term properties of families of maps of topological spaces. Abstract topological dynamics is usually developed in the context of flows. [64%] 2021-12-21 [Mappings] [Dynamical Systems]...
12. Topological manifold: In topology, a branch of mathematics, a topological manifold is a topological space that locally resembles real n-dimensional Euclidean space. Topological manifolds are an important class of topological spaces, with applications throughout mathematics. [64%] 2023-03-12 [Manifolds] [Properties of topological spaces]...
13. Topological ring: A topological ring is a ring $R$ that is a topological space, and such that the mappings \[ (x,y) \mapsto x-y \] and \[ (x,y) \mapsto xy \] are continuous. A topological ring $R$ is called separated if it is separated ... (Mathematics) [64%] 2023-10-26
14. Topological order: In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of ... (Physics) [64%] 2022-09-26 [Quantum phases] [Condensed matter physics]...
15. Topological conjugacy: In mathematics, two functions are said to be topologically conjugate if there exists a homeomorphism that will conjugate the one into the other. Topological conjugacy, and related-but-distinct § Topological equivalence of flows, are important in the study of iterated ... [64%] 2022-12-01 [Homeomorphisms]
16. Topological property: In topology and related areas of mathematics, a topological property or topological invariant is a property of a topological space that is invariant under homeomorphisms. Alternatively, a topological property is a proper class of topological spaces which is closed under ... (Mathematical property of a space) [64%] 2022-09-24 [Properties of topological spaces] [Homeomorphisms]...
17. Topological structure (topology): open topology, respectively, closed topology A collection $\mathfrak G$, respectively $\mathfrak F$, of subsets of a set $X$, satisfying the following properties: $1$. The set $X$, as well as the empty set $\emptyset$, are elements of the collection $\mathfrak G ... (Topology) [64%] 2023-09-10 [General topology]
18. Topological polymers: Topological polymers may refer to a polymeric molecule that possesses unique spatial features, such as linear, branched, or cyclic architectures. It could also refer to polymer networks that exhibit distinct topologies owing to special crosslinkers. (Chemistry) [64%] 2023-10-21 [Polymers]
19. Topological skeleton: In shape analysis, skeleton (or topological skeleton) of a shape is a thin version of that shape that is equidistant to its boundaries. The skeleton usually emphasizes geometrical and topological properties of the shape, such as its connectivity, topology, length ... [64%] 2023-06-27 [Image processing] [Digital geometry]...