metric space 2 Let F be a closed set for k = 1, 2,..., n in (S, d). Show that U F, is closed.k=13 Give an example to show that the arbitrary intersection of open sets is not anopen set.4 Prove that if A is nowhere dense in discrete space (S, d) then A = 0.5 Prove that a closed set in the metric space (S, d) either is nowhere dense in S or elsecontains some nonempty open set.

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2 Let F be a closed set for k = 1, 2, ... , n in (S, d). Show that |J F, is closed. k=1

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 27E: 27. Let , where and are nonempty. Prove that has the property that for every subset of if and...

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Question

metric space

2 Let F be a closed set for k = 1, 2,
..., n in (S, d). Show that U F, is closed.
k=1
3 Give an example to show that the arbitrary intersection of open sets is not an
open set.
4 Prove that if A is nowhere dense in discrete space (S, d) then A = 0.
5 Prove that a closed set in the metric space (S, d) either is nowhere dense in S or else
contains some nonempty open set.

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