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Elements Of Modern Algebra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 29E: 29. Suppose , , represents a partition of the nonempty set A. Define R on A by if and only if there...

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and let
Let X be an mpinite set
topolegy
of X
X in which all
be a
on
inginite Subset
(hat
X are
open.
discrete topology
Show
tis
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on X-

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29. Suppose , , represents a partition of the nonempty set A. Define R on A by if and only if there is a subset such that . Prove that R is an equivalence relation on A and that the equivalence classes of R are the subsets .
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Can a topology on an infinite set not be discrete and indiscrete in which every subset is clopen?
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