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发帖数: 299 | 1 Using the definition of compactness to prove: If s is a compact subset of R
and T is a closed subset of S, then T is compact.
Definition of compact set: A set S is said to be compact if whenever it is
contained in the union of a family F of open sets, then it is contained in
the union of some finite number of the sets in F. If F is a family of open
sets whose union contains S, then F is called an open cover of S. If Y<=F
and Y is also an open cover of S, then Y is called a sub cover of S. thus S |
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