Let x be 1. Let X be a topological space and be an equivalence relation on the elements of X. Define : X→ X/~ byT(x) = [x],i.e. 7 sends an element to its equivalence class. Let T be the collection of all subsets U of X/ such that -¹(U) is open in X.(a) Show that the map 7 defined above is continuous.

Answered: 1. Let X be a topological space and be…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.3: Subgroups

Problem 23E: 23. Let be the equivalence relation on defined by if and only if there exists an element in ...

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23. Let be the equivalence relation on defined by if and only if there exists an element in such that .If , find , the equivalence class containing.
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1. Let X be a topological space and be an equivalence relation on the elements of X. Define : XX/~ by π(x) = [x], i.e. sends an element to its equivalence class. Let T be the collection of all subsets U of X/ such that 7-¹(U) is open in X. (a) Show that the map 7 defined above is continuous.