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 afunction f:(X,r) (Y,A) is continuous if and only if theinverse image under f of every A- closed set is a r-closed set.

Answered: 1. Let (X,r) and (Y,A) be two…

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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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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