Difference between revisions of "Regular topological space"
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==[[Regular topological space/Definition|Definition]]== | ==[[Regular topological space/Definition|Definition]]== | ||
{{:Regular topological space/Definition}} | {{:Regular topological space/Definition}} | ||
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==See also== | ==See also== | ||
* [[Topological separation axioms]] | * [[Topological separation axioms]] | ||
Latest revision as of 23:53, 3 May 2016
Contents
[hide]Definition
A topological space, (X,J) is regular if[1]:
- ∀E∈C(J) ∀x∈X−E ∃U,V∈J[U∩V=∅⟹(E⊂U∧x∈V)] - (here C(J) denotes the closed sets of the topology J)
Warning:Note that it is E⊂U not ⊆, the author ([1]) like me is pedantic about this, so it must matter
TODO: Investigate consequences/differences between E⊆U and E⊂U
TODO: Picture
See also
References
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