Problem 5. Prove that the space X is Hausdorff if and only if the set ▲ = {(x,x) : x ¤ X} is closed in X × X.
Problem 5. Prove that the space X is Hausdorff if and only if the set ▲ = {(x,x) : x ¤ X} is closed in X × X.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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![Problem 5. Prove that the space X is Hausdorff if and only if the set
▲ = {(x,x) : x = X} is closed in X × X.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feabade52-5174-4cc3-8205-365538407c90%2F4facf237-40b6-4b35-ba32-07606158fa5c%2Ffvqt31j_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 5. Prove that the space X is Hausdorff if and only if the set
▲ = {(x,x) : x = X} is closed in X × X.
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