7. Let H ~ Rn. (a) Prove that H is compact if and only if every cover

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7. Let H ~ Rn.

(a) Prove that H is compact if and only if every cover {E"}"EA of H, where the E,,'s are relatively open in H, has a finite sub covering.

(b) Use part (a), Exercise 6a, p. 276, and Definition 9.9 to show directly that if f : H -+ Rm is continuous and H is compact, then f(H) is compact

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An Introduction To Analysis

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Authors: William R. Wade

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Question Posted: Jul 18, 2024 10:14 AM

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7. Let H ~ Rn. (a) Prove that H is compact if and only if every cover

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An Introduction To Analysis

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