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

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

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 23E: Let a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove...

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Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Let X be a discrete spaces then *
X is never homeomorphic to R
X is homeomorphic to R if and only if X is finite
X is homeomorphic to R if and only if X is infinite
O X is homeomorphic to R if and only if X is countable
2r 1. r<2
2r- 1. rNN
Let f: R R be defined by f(r)

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