Urysohn's lemma

Stub grade: B

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Statement

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

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

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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