topology

GPTKB entity

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