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Let (X, d) be a metric space and let y be a compact subset of X. Show that Y is closed and bounded.

Let (X, d) be a metric space and let y be a compact subset of X. Show that Y is closed and bounded.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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(a) Let (X, d) be a metric space and let Y be a compact subset of X. Show that Y is closed and bounded. (b) Let X be an infinite set with the discrete metric d(x, y) = = 1, if x #y, 0. if x = y. 12 Prove that any infinite subset Y CX is closed and bounded, but not compact.
Transcribed Image Text:(a) Let (X, d) be a metric space and let Y be a compact subset of X. Show that Y is closed and bounded. (b) Let X be an infinite set with the discrete metric d(x, y) = = 1, if x #y, 0. if x = y. 12 Prove that any infinite subset Y CX is closed and bounded, but not compact.
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