1\Show that for any collection of topologies on X there exist a unique smallest toplogylarger than each member of the collection.2\Let X be a non empty set and F be a family of subsets of X such thatF1:0, X E FF2: F1, F2 E F then F1 UF₂ EFF3:F, EF for any λEA then n {F2: λ EA} EFShow that there exists a unique topology for X such that T-closed of subsets of X areprecisely the member of F.M)جات

1. Unique Smallest Topology Larger Than Each Member of a CollectionFor any collection of topologies…

Answered: 1\Show that for any collection of…

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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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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