Let R have its usual topology and let X = {a,b, c}. Define ƒ : R→ X byx < 0a,f(æ) =b, x = 0c,x > 0Is X with the quotient topology Hausdorff? Justify your answer.

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Answered: Let R have its usual topology and let X…

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

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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Question

Let R have its usual topology and let X = {a,b, c}. Define ƒ : R→ X by
x < 0
a,
f(æ) =
b, x = 0
c,
x > 0
Is X with the quotient topology Hausdorff? Justify your answer.

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