Normal topological space

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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


  1. Introduction to Topology - Theodore W. Gamelin & Robert Everist Greene