Let A and B be any two subsets of a metric space (X, d). Then (1) A is a closed set. (2) If ACB, then A C B. (3) A is the smallest closed superset of A.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.4: Linear Programming
Problem 8E
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Solve subparts (1) and (3)
Let A and B be any two subsets of a metric space (X, d). Then
(1) A is a closed set.
obsu
(2) If ACB, then AC B.
(3) A is the smallest closed superset of A.
(4) A = A if and only if A is closed.
(5) A is the intersection of all closed sets containing A.
(6) AUB = ĀUB
%3D
(7) ANBCA OB
Transcribed Image Text:Let A and B be any two subsets of a metric space (X, d). Then (1) A is a closed set. obsu (2) If ACB, then AC B. (3) A is the smallest closed superset of A. (4) A = A if and only if A is closed. (5) A is the intersection of all closed sets containing A. (6) AUB = ĀUB %3D (7) ANBCA OB
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