Please answer e and f only 2-5. For each of the following properties, give an example consisting of two sub-sets X, Y CR2, both considered as topological spaces with their Euclideantopologies, together with a map f: X → Y that has the indicated property.(a) f is open but neither closed nor continuous.(b) f is closed but neither open nor continuous.(c) f is continuous but neither open nor closed.(d) f is continuous and open but not closed.(e) f is continuous and closed but not open.(f) f is open and closed but not continuous.

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Answered: (e) f is continuous and closed but not…

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(e) f is continuous and closed but not open. (f) f is open and closed but not continuous.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.3: Properties Of Composite Mappings (optional)

Problem 9E: Find mappings f,g and h of a set A into itself such that fg=hg and fh. Find mappings f,g and h of a...

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