If f (X,c)——(Y .A) and g :(Y .A)——>(Z I) are closed functions, prove that g °f :(¥ ,¢)——+(Z,1) is closed function. 4. If f :(X,r)-(Y.A) and g:(Y.A) (Z.r)are closed functions,prove that gof :(X.r)(Z.r) is closed function.

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4. If f:(X,r)(Y.A) and g:(Y.A) (Z,r)are closed functions, prove that g of :(X.r)(Z.r) is closed function.

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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If f (X,c)——(Y .A) and g :(Y .A)——>(Z I) are closed functions, prove that g °f :(¥ ,¢)——+(Z,1) is closed function.

4. If f :(X,r)-(Y.A) and g:(Y.A) (Z.r)are closed functions,
prove that gof :(X.r)(Z.r) is closed function.

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