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Graduate Topology Study Notes (1)

Problem: Given U: open, K: compact, U is contained in K, both are contained in Hausdroff space X. Also given a continuous map f from a Hausdroff space X to another Hausdroff space Y, prove that the closure of the mapping space f(U) is a compact subest of f(K). Further, given f is an onto, open mapping, and X is locally companct, prove that Y is also locally compact.
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topology_notes_hausdorff_locally_compact


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