Difference between revisions of "Urysohn's lemma"
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Latest revision as of 00:21, 4 May 2016
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
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Not an easy proof
References
