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Exercise 6. Suppose K is a compact subset of the metric space (X, d). a) Show that for each x E X, there is a point k, such that d(x, k₂) = dk (t) = d(r, K) = inf d(k, r). KEK

Exercise 6. Suppose K is a compact subset of the metric space (X, d). a) Show that for each x E X, there is a point k, such that d(x, k₂) = dk (t) = d(r, K) = inf d(k, r). KEK

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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Exercise 6. Suppose K is a compact subset of the metric space (X, d). a) Show that for each x E X, there is a point k, such that WIL that d(x, k₂) = dk (x) = d(x, K) = inf d(k, x). KEK
Transcribed Image Text:Exercise 6. Suppose K is a compact subset of the metric space (X, d). a) Show that for each x E X, there is a point k, such that WIL that d(x, k₂) = dk (x) = d(x, K) = inf d(k, x). KEK
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