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Up: 18.100B, Fall 2002 In-class
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Prove that in any metric space, a finite union of
compact subsets is compact.
be a finite collection of compact
sets in a metric space
be their union. An
covers each of the
assumed compactness there is a finite subcover
All these sets
taken together give a finite subcover of
which is therefore compact.
Richard B. Melrose