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a metric space (M, d) s.t. the set A = {1} is not open in (M, d)

a metric space (M, d) s.t. the set A = {1} is not open in (M, d)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Give an example of each of the following or prove that such a request is impossible. a metric space (M, d) s.t. the set A = {1} is not open in (M, d) d) real numbers x, y s.t. there exist two disjoint neighborhoods of these numbers. e) infinite family of open sets S₁ S₂ 2... whose intersections; is closed and nonempty.
Transcribed Image Text:Give an example of each of the following or prove that such a request is impossible. a metric space (M, d) s.t. the set A = {1} is not open in (M, d) d) real numbers x, y s.t. there exist two disjoint neighborhoods of these numbers. e) infinite family of open sets S₁ S₂ 2... whose intersections; is closed and nonempty.
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