Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Let (¥,r) and (¥ ,4) be two topological spaces. Prove that a function f :(X .r)——(¥ ,A) is continuous if and only if the inverse image under / of every A- closed set is a r- closed set.

1. Let (X,r) and (Y ,A) be two topological spaces. Prove that a function f:(X,r) (Y,A) is continuous if and only if the inverse image under f of every A- closed set is a r-closed set.
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Transcribed Image Text:1. Let (X,r) and (Y ,A) be two topological spaces. Prove that a function f:(X,r) (Y,A) is continuous if and only if the inverse image under f of every A- closed set is a r-closed set.
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