Normal topological space/Definition
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< Normal topological space
Revision as of 00:00, 4 May 2016 by Alec (Talk | contribs) (Created page with "<noinclude> ==Definition== </noinclude>A topological space, {{Top.|X|J}}, is said to be ''normal'' if{{rITTGG}}: * {{M|1=\forall E,F\in C(\mathcal{J})\ \exists U,V\in\math...")
Definition
A topological space, [ilmath](X,\mathcal{ J })[/ilmath], is said to be normal if[1]:
- [ilmath]\forall E,F\in C(\mathcal{J})\ \exists U,V\in\mathcal{J}[E\cap F=\emptyset\implies(U\cap V=\emptyset\wedge E\subseteq U\wedge F\subseteq V)][/ilmath] - (here [ilmath]C(\mathcal{J})[/ilmath] denotes the collection of closed sets of the topology, [ilmath]\mathcal{J} [/ilmath])
