Urysohn's lemma

Stub grade: B

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Statement

Let [ilmath](X,\mathcal{ J })[/ilmath] be a normal topological space, let [ilmath]E[/ilmath] and [ilmath]F[/ilmath] be a pair of disjoint closed sets of [ilmath]X[/ilmath], then:

• there exists a continuous function, [ilmath]f:X\rightarrow [0,1]\subset\mathbb{R} [/ilmath] such that [ilmath]f[/ilmath] is [ilmath]0[/ilmath] on [ilmath]E[/ilmath] and [ilmath]f[/ilmath] is [ilmath]1[/ilmath] on [ilmath]F[/ilmath]

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TODO: Get a picture - the idea of this theorem is brilliant, once you see it!

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Proof

Grade: C

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Not an easy proof