# Urysohn's lemma

From Maths

**Stub grade: B**

This page is a stub

This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.

## 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^{[1]}:

- 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]

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

## Proof

Grade: C

This page requires one or more proofs to be filled in, it is on a to-do list for being expanded with them.

Please note that this does not mean the content is unreliable. Unless there are any caveats mentioned below the statement comes from a reliable source. As always, Warnings and limitations will be clearly shown and possibly highlighted if very important (see template:Caution et al).

The message provided is:

The message provided is:

Not an easy proof

## References