Difference between revisions of "Normal topological space"
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==[[Normal topological space/Definition|Definition]]== | ==[[Normal topological space/Definition|Definition]]== | ||
{{:Normal topological space/Definition}} | {{:Normal topological space/Definition}} | ||
| + | ==Equivalent statements== | ||
| + | * [[A topological space is normal if and only if for each closed set, E, and each open set, W, containing E there exists an open set U containing E such that the closure of U is strictly a subset of W]] | ||
| + | {{Todo|Make that sentence easier to read}} | ||
==See also== | ==See also== | ||
* [[Topological separation axioms]] | * [[Topological separation axioms]] | ||
Revision as of 00:12, 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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