Properties (54)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Architect
|
| gptkbp:hasExhibition |
Real numbers under addition with standard topology
Circle_group_under_multiplication |
| gptkbp:hasRelatedPatent |
Used in algebraic topology
Used in representation theory Used in differential geometry Used in functional analysis Used in harmonic analysis |
| gptkbp:hasSpecialty |
Connected groups
Closure under group operation Abelian groups are topological groups Combines topology and group theory Compact groups Continuous group operations Examples include abelian groups Examples include affine groups Examples include algebraic groups Examples include automorphism groups Examples include compact Lie groups Examples include connected groups Examples include discrete groups Examples include free groups Examples include homeomorphism groups Examples include isometry groups Examples include linear groups Examples include locally compact groups Examples include matrix groups Examples include non-abelian groups Examples include projective groups Examples include semidirect products Examples include symmetry groups Examples include topological abelian groups Examples include topological fields Examples include topological monoids Examples include topological non-abelian groups Examples include topological rings Examples include topological semigroups Examples include topological vector spaces Examples include transformation groups Existence of identity element Existence of inverses Group homomorphisms are continuous Locally compact groups Non-Abelian groups can also be topological groups Quotient groups can be topological groups Subgroups can be topological groups Topology is compatible with group structure Examples_include_Polish_groups Hausdorff_condition |
| gptkbp:hasTheme |
Urysohn's lemma
Lie's theorem Bourbaki's_theorem_on_topological_groups Tychonoff's_theorem |
| https://www.w3.org/2000/01/rdf-schema#label |
Topological Groups
|