Let M,N,O ⊆ X, d be non-empty open sets in a metric space X. Prove the following: M ⋃ N ⋃ O is open in X. M ⋂ N ⋂ C is open in X.
Let M,N,O ⊆ X, d be non-empty open sets in a metric space X. Prove the following: M ⋃ N ⋃ O is open in X. M ⋂ N ⋂ C is open in X.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 22E
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Let M,N,O ⊆ X, d be non-empty open sets in a metric space X. Prove the following:
- M ⋃ N ⋃ O is open in X.
- M ⋂ N ⋂ C is open in X.
Note: You cannot use the theorem that the union of open sets is open and the finite intersection of open sets is open.
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