Recall that RK denotes the real line with the K-topology. Let Y denote the quotient space obtained from RK by collapsing the set K to a point. Prove that Y satisfies the T1 axiom, but is not Hausdorff.

Recall that RK denotes the real line with the K-topology. Let Y denote the quotient space obtained from RK by collapsing the set K to a point. Prove that Y satisfies the T1 axiom, but is not Hausdorff.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 18E: Let (A) be the power set of the nonempty set A, and let C denote a fixed subset of A. Define R on...

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Question

Recall that RK denotes the real line with the K-topology. Let Y
denote the quotient space obtained from RK by collapsing the set K
to a point. Prove that Y satisfies the T axiom, but is not Hausdorff.

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