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Statements (164)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
gptkb:group_of_people gptkb:mathematical_concept gptkb:topology mathematical discipline |
| gptkbp:alternativeName |
Topological_space
Topologie algebraic_topology metric_space topological_construction topological_group topological_invariant topological_manifold topological_property topological_space topos |
| gptkbp:appliesTo |
gptkb:geometry
computer science mathematical analysis physics |
| gptkbp:concerns |
continuity
compactness homeomorphism connectedness open sets |
| gptkbp:definedIn |
gptkb:Metric
group with topology such that multiplication and inversion are continuous |
| gptkbp:etymology |
Greek 'topos' (place) and 'logos' (study)
|
| gptkbp:example |
gptkb:discrete_metric_space
gptkb:circle_group real numbers with absolute value metric space of continuous functions with supremum metric discrete group with discrete topology general linear group with standard topology p-adic numbers with addition real numbers with addition |
| gptkbp:field |
gptkb:mathematics
|
| gptkbp:generalizes |
gptkb:Euclidean_space
gptkb:normed_vector_space |
| gptkbp:hasApplication |
gptkb:Lie_theory
harmonic analysis number theory representation theory |
| gptkbp:hasAxiom |
gptkb:symmetry
identity of indiscernibles non-negativity triangle inequality |
| gptkbp:hasConcept |
gptkb:Hilbert_space
gptkb:Gromov–Hausdorff_distance gptkb:Polish_space completeness Cauchy sequence Hausdorff space boundedness closed ball closed set compactness completion convergence dense subset diameter geodesic metric space homeomorphism isometric embedding isometry length space limit point metric topology open ball open set product metric space pseudometric space quasimetric space quotient metric space separability separable space subspace totally bounded ultrametric space |
| gptkbp:hasProperty |
distance function
can be compact or non-compact homogeneous space Hausdorff (often assumed) can be Lie group can be Polish group can be abelian group can be compact group can be connected group can be connected or disconnected can be discrete group can be locally compact can be locally connected group can be metrizable can be nilpotent group can be non-abelian can be path-connected group can be profinite group can be second-countable can be separable can be sigma-compact can be simple group can be simply connected group can be solvable group can be totally disconnected can be totally disconnected group group operation is continuous inversion is continuous |
| https://www.w3.org/2000/01/rdf-schema#label |
topology
|
| gptkbp:includes |
gptkb:point-set_topology
gptkb:topology differential topology geometric topology |
| gptkbp:introducedIn |
20th century
|
| gptkbp:notablePerson |
gptkb:Felix_Hausdorff
gptkb:Henri_Poincaré gptkb:John_Milnor |
| gptkbp:originatedIn |
late 19th century
|
| gptkbp:relatedTo |
gptkb:fundamental_group
gptkb:set_theory gptkb:Brouwer_fixed-point_theorem homology fixed-point theorem knot theory covering space homotopy topological spaces metric spaces manifolds topological invariants |
| gptkbp:studiedIn |
gptkb:topology
abstract algebra |
| gptkbp:studies |
properties of space preserved under continuous deformations
|
| gptkbp:subclassOf |
gptkb:Lie_group
profinite group compact group discrete group abelian topological group locally compact group |
| gptkbp:usedIn |
gptkb:topology
analysis |
| gptkbp:bfsParent |
gptkb:Michael_Freedman
gptkb:Alfred_Tarski gptkb:Friedrich_Hirzebruch gptkb:Hilbert_space gptkb:Jean-Pierre_Serre gptkb:Mathematics gptkb:Max_Dehn gptkb:Michael_Atiyah gptkb:Poul_Heegaard gptkb:algebra gptkb:butter gptkb:geometry gptkb:group_of_people gptkb:network_protocol gptkb:Sergei_Novikov gptkb:Simon_Donaldson gptkb:fiber gptkb:John_W._Milnor gptkb:Barry_Mazur gptkb:Dennis_Sullivan gptkb:Grigori_Perelman gptkb:John_Milnor gptkb:Peter_Teichner |
| gptkbp:bfsLayer |
4
|