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What Does Compactness Really Mean? - Scientific American Blog …
http://at.yorku.ca/b/ask-an-analyst/2003/0554.htm Websets if every decreasing sequence of closed, nonempty sets has nonempty intersection. Theorem 8. A metric space is sequentially compact if and only if it has the nite intersection property for closed sets. Proof. Suppose that Xis sequentially compact. Given a decreasing sequence of closed sets F n, choose x n2F nfor each n2N. Then (x n) has a ... for thinking
Proving that the Union of Two Compact Sets is Compact
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