T1 separation axiom

GPTKB entity

Statements (18)
Predicate Object
gptkbp:instanceOf gptkb:topology
gptkbp:alsoKnownAs gptkb:Fréchet_space
accessible space
gptkbp:appliesTo topological spaces
gptkbp:defines A topological space is T1 if for every pair of distinct points, each has a neighborhood not containing the other.
https://www.w3.org/2000/01/rdf-schema#label T1 separation axiom
gptkbp:implies gptkb:T2_separation_axiom
all singletons are closed
finite sets are closed
gptkbp:introduced gptkb:Felix_Hausdorff
gptkbp:introducedIn 1920s
gptkbp:isWeakerThan gptkb:T0_separation_axiom
gptkb:T2_separation_axiom
gptkbp:relatedTo separation axioms
gptkbp:symbol T1
gptkbp:usedIn gptkb:general_topology
gptkbp:bfsParent gptkb:T0_separation_axiom
gptkbp:bfsLayer 7