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
Definition
A topological space, [ilmath](X,\mathcal{ J })[/ilmath] is regular if[1]:
- [ilmath]\forall E\in C(\mathcal{J})\ \forall x\in X-E\ \exists U,V\in\mathcal{J}[U\cap V=\emptyset\implies(E\subset U\wedge x\in V)][/ilmath] - (here [ilmath]C(\mathcal{J})[/ilmath] denotes the closed sets of the topology [ilmath]\mathcal{J} [/ilmath])
Warning:Note that it is [ilmath]E\subset U[/ilmath] not [ilmath]\subseteq[/ilmath], the author ([1]) like me is pedantic about this, so it must matter
TODO: Investigate consequences/differences between [ilmath]E\subseteq U[/ilmath] and [ilmath]E\subset U[/ilmath]
TODO: Picture
See also
References
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