1- In a metric space (X, d), if A and A2 are open subsets of X then A1 U A2 is open in X. 2- In a metric space (X, d), A is the intersection of all closed subsets of X which contains A. 3- In a complete metric space (X, d), If A C X such that, A = A then A is complete as a sub space of X.

1- In a metric space (X, d), if A and A2 are open subsets of X then A1 U A2 is open in X. 2- In a metric space (X, d), A is the intersection of all closed subsets of X which contains A. 3- In a complete metric space (X, d), If A C X such that, A = A then A is complete as a sub space of X.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter7: Real And Complex Numbers

Section7.2: Complex Numbers And Quaternions

Problem 48E

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Question

1- In a metric space (X, d), if A1 and A2 are open subsets of X then
A1 U A2 is open in X.
2- In a metric space (X, d), A is the intersection of all closed subsets
of X which contains A.
3- In a complete metric space (X, d), If AC X such that, A = A then
A is complete as a sub space of X.

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