Difference between revisions of "Regular topological space"

Revision as of 23:46, 3 May 2016

Definition

A topological space, $(X,\mathcal{ J })$ is regular if^[1]:

• $\forall E\in C(\mathcal{J})\ \forall x\in X-E\ \exists U,V\in\mathcal{J}[U\cap V=\emptyset\implies(E\subset U\wedge x\in V)]$ - (here $C(\mathcal{J})$ denotes the closed sets of the topology $\mathcal{J}$)

Warning:Note that it is $E\subset U$ not $\subseteq$, the author (^[1]) like me is pedantic about this, so it must matter

See also

• Topological separation axioms
• Normal topological space

References

1. ↑ ^{<cite_references_link_many_accessibility_label> 1.0 1.1} Introduction to Topology - Theodore W. Gamelin & Robert Everist Greene