Difference between revisions of "Compact"
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A continuous image of a compact space is compact. That is, if X,Y are topological spaces, and if X is compact and f: X → Y is a continuous surjective function, then Y is compact. | A continuous image of a compact space is compact. That is, if X,Y are topological spaces, and if X is compact and f: X → Y is a continuous surjective function, then Y is compact. | ||
Revision as of 19:06, 7 December 2022
(EVT = Extreme Value Theorem)
A continuous image of a compact space is compact. That is, if X,Y are topological spaces, and if X is compact and f: X → Y is a continuous surjective function, then Y is compact.
