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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let x be
![1. Let X be a topological space and be an equivalence relation on the elements of X. Define : X→ X/~ by
T(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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff105aa48-49da-419d-a72b-e6b903f945eb%2F6e49b0b8-ef3a-44a9-8cad-9cd50eac92f2%2Fyt3mnsb_processed.png&w=3840&q=75)
Transcribed Image Text:1. Let X be a topological space and be an equivalence relation on the elements of X. Define : X→ X/~ by
T(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.
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