Difference between revisions of "Normal topological space"
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* [[Topological separation axioms]] | * [[Topological separation axioms]] | ||
* [[Regular topological space]] | * [[Regular topological space]] | ||
| + | * [[Urysohn's lemma]] | ||
| + | * [[Tietze extension theorem]] | ||
==References== | ==References== | ||
<references/> | <references/> | ||
{{Topology navbox|plain}} | {{Topology navbox|plain}} | ||
{{Definition|Topology}} | {{Definition|Topology}} | ||
Latest revision as of 00:14, 4 May 2016
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])
Equivalent statements
TODO: Make that sentence easier to read
See also
References
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