Let R have its usual topology and let X = {a, b, c}. Define f : R →X byа,x < 0f(x) = { b,x = 0%3Dс,x >0A. Fully describe the quotient topology on X induced by f.B. Is X with the quotient topology Hausdorff? Justify your answer.

Given, ℝ have its usual topology and let X=a, b, c. Define f: ℝ→X by…

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Let R have its usual topology and let X = {a,b, c}. Define f : R –→ X by а, х<1 f(x) = b, x = с, x >

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 6E

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Question

Let R have its usual topology and let X = {a, b, c}. Define f : R →X by
а,
x < 0
f(x) = { b,
x = 0
%3D
с,
x >0
A. Fully describe the quotient topology on X induced by f.
B. Is X with the quotient topology Hausdorff? Justify your answer.

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