Re: disjoint subsets compact subsets
- From: The World Wide Wade <aderamey.addw@xxxxxxxxxxx>
- Date: Wed, 30 Jan 2008 16:38:29 -0800
In article <fnqv54$o6r$1@xxxxxxxxxxxxxxxxx>, "Asfer" <asfer@xxxxxxxx>
wrote:
Let Y be a Hausdorff compact space.
Let C be a compact subspace of Y.
Let W and V be disjoint open sets of Y, where W contains C.
Then the closure of V in Y is disjoint from C. Why?
Y \ W is closed and contains V, hence contains the closure of V. So
the closure of V is disjoint from W, hence is disjoint from C. (This
has nothing to do with Hausdorff spaces or compactness.)
.
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- disjoint subsets compact subsets
- From: Asfer
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