Could you explain how to show 7.13 in detail? Definition. Let X and Y be topological spaces. A function or map f : X → Y is acontinuous function or continuous map if and only if for every open set U in Y,f-'(U) is open in X.Definition. Let f : X → Y be a function between topological spaces X and Y, andlet x e X. Then f is continuous at the point x if and only if for every open setV containing f(x), there is an open set U containing x such that f(U) c V. Thus afunction f : X → Y is continuous if and only if it is continuous at each point.Theorem 7.13. Let f : X → Y be a function and let B be a basis for Y. Then f iscontinuous if and only if for every open set B in B, f-'(B) is open in X.

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Description: Could you explain how to show 7.13 in detail? Definition. Let X and Y be topological spaces. A function or map f : X → Y is acontinuous function or continuous map if and only if for every open set U in Y,f-'(U) is open in X.Definition. Let f : X → Y

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topological spaces X and Y,

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 6E: 6. a. Give an example of mappings and , different from those in Example , where is one-to-one, is...

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