Exercise 6. Suppose K is a compact subset of the metric space (X, d). that d) To simplify notations, we will also denote by d+∞o the metric dmax on R". Endow R" with anyone of the metrics dp, p = [1, +∞o]. If C C R is a closed non-empty subset of R", show that there is a kc EC such that dp(x, kc) = dp(x, C) = inf dp(x,c).
Exercise 6. Suppose K is a compact subset of the metric space (X, d). that d) To simplify notations, we will also denote by d+∞o the metric dmax on R". Endow R" with anyone of the metrics dp, p = [1, +∞o]. If C C R is a closed non-empty subset of R", show that there is a kc EC such that dp(x, kc) = dp(x, C) = inf dp(x,c).
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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6d
![Exercise 6. Suppose K is a compact subset of the metric space (X, d).
that
d) To simplify notations, we will also denote by d+00 the metric dmax on R". Endow R
with anyone of the metrics dp, p = [1, +∞o]. If C C R is a closed non-empty subset of R", show
that there is a kc EC such that
dp(x, kc) = dp(x, C) = inf dp(x, c).
CEC](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a4dcd82-baf4-45bc-b40b-693a3e683492%2F3db533e1-b1ea-4c27-a2a9-568f9dfbe367%2Fxbeq7ec_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 6. Suppose K is a compact subset of the metric space (X, d).
that
d) To simplify notations, we will also denote by d+00 the metric dmax on R". Endow R
with anyone of the metrics dp, p = [1, +∞o]. If C C R is a closed non-empty subset of R", show
that there is a kc EC such that
dp(x, kc) = dp(x, C) = inf dp(x, c).
CEC
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