Let X be a discrete spaces then O X is homeomorphic to R if and. only if X is countable O X is homeomorphic to R if and only if X is finite X is never homeomorphic to R O X is homeomorphic to R if and only if X is infinite

Let X be a discrete spaces then O X is homeomorphic to R if and. only if X is countable O X is homeomorphic to R if and only if X is finite X is never homeomorphic to R O X is homeomorphic to R if and only if X is infinite

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.4: Binary Operations

Problem 11E

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Question

Let X be a discrete spaces then
O X is homeomorphic to R if and.only if X is countable
O X is homeomorphic to R if and only if X is finite
OXis never homeomorphic to R
O Xis homeomorphic to Rif and only if X is infinite

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