Suppose A is a closed, non-empty subset of a metric space (X, d) and p a point of X which is not in A. Prove that inf{d(p, a) : a € A} is positive (that is it is not zero).
Suppose A is a closed, non-empty subset of a metric space (X, d) and p a point of X which is not in A. Prove that inf{d(p, a) : a € A} is positive (that is it is not zero).
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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Transcribed Image Text:Suppose A is a closed, non-empty subset of a metric space (X, d) and p a point
of X which is not in A. Prove that inf{d(p, a) : a € A} is positive (that is it is
not zero).
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Given: A is a closed and non-empty set of a metric space (X,d) and .
To Prove: .
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