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(b) Prove that the intersection of finite collection of open sets in the metric space (M, d) is open set in M. But the intersection of any collection of open sets in (M,d) need not to be open set in M, explain that.

(b) Prove that the intersection of finite collection of open sets in the metric space (M, d) is open set in M. But the intersection of any collection of open sets in (M,d) need not to be open set in M, explain that.

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 20E: Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not...
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(b) Prove that the intersection of finite collection of open sets in the metric space (M, d) is open set in M. But the intersection of any collection of open sets in (M, d) need not to be open set in M, explain that.
Transcribed Image Text:(b) Prove that the intersection of finite collection of open sets in the metric space (M, d) is open set in M. But the intersection of any collection of open sets in (M, d) need not to be open set in M, explain that.
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