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.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 26E: 26. Let and. Prove that for any subset of T of .

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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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