Statements (79)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:defines |
A group equipped with a topology such that the group operations are continuous
|
| gptkbp:example |
gptkb:Lie_groups
gptkb:Circle_group gptkb:Discrete_groups gptkb:Real_numbers_under_addition gptkb:Unitary_group General linear group |
| gptkbp:field |
gptkb:Mathematics
|
| gptkbp:hasApplication |
gptkb:Physics
gptkb:Number_theory gptkb:Algebraic_geometry gptkb:Representation_theory gptkb:Differential_geometry Harmonic analysis |
| gptkbp:hasSubfield |
gptkb:Topology
gptkb:Group_theory gptkb:Topological_vector_spaces gptkb:Lie_groups gptkb:Algebraic_groups gptkb:Discrete_groups gptkb:Locally_compact_groups gptkb:Profinite_groups Abelian topological groups Compact groups Connected groups Linear groups Matrix groups Nilpotent groups Simple groups Solvable groups Topological Artin groups Topological Coxeter groups Topological Galois groups Topological Hecke groups Topological abelian groups Topological automorphism groups Topological braid groups Topological covering groups Topological crystallographic groups Topological diffeomorphism groups Topological dynamical systems Topological endomorphism groups Topological fields Topological fundamental groups Topological groupoids Topological homeomorphism groups Topological isometry groups Topological knot groups Topological mapping class groups Topological modular groups Topological modules Topological monoids Topological permutation groups Topological point groups Topological reflection groups Topological rings Topological semigroups Topological space groups Topological symmetry groups Topological transformation groups Topological wallpaper groups Totally disconnected groups p-adic groups |
| https://www.w3.org/2000/01/rdf-schema#label |
Topological Groups
|
| gptkbp:introduced |
gptkb:Felix_Hausdorff
|
| gptkbp:introducedIn |
1920s
|
| gptkbp:property |
Group multiplication is continuous
Inversion is continuous |
| gptkbp:relatedConcept |
gptkb:group_of_people
gptkb:topology gptkb:Homomorphism gptkb:Lie_group Continuous function |
| gptkbp:relatedGroup |
Multiplication
Inversion |
| gptkbp:studiedIn |
gptkb:Algebraic_topology
|
| gptkbp:bfsParent |
gptkb:Lev_Pontryagin
|
| gptkbp:bfsLayer |
5
|