Could you explain how to show 7.10 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.AU B, where A, B are closed in X. Let ƒ :Theorem 7.10 (Pasting lemma). Let X =A → Y and g : B → Y be continuous functions that agree on An B. Then the functionh: AUB → Y defined by h = f on A and h = g on B is continuous.

Name: Could you explain how to show 7.10 in detail? Definition. Let X and Y
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Description: Could you explain how to show 7.10 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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Theorem 7.10 (Pasting lemma). Let X = A U B, where A, B are closed in X. Let f : A → Y and g : B → Y be continuous functions that agree on A ŋ B. Then the function h : AUB → Y defined by h = ƒ on A and h = g on B is continuous.

Theorem 7.10 (Pasting lemma). Let X = A U B, where A, B are closed in X. Let f : A → Y and g : B → Y be continuous functions that agree on A ŋ B. Then the function h : AUB → Y defined by h = ƒ on A and h = g on B is 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 6E: 6. a. Give an example of mappings and , different from those in Example , where is one-to-one, is...

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