3.6.3. Let || ||a and || || be equivalent norms on a vector space X, and let E be a subset of X. For each of the following statements, prove that the statement is true with respect to ||- ||a if and only if it is true with respect to ||- ||b. (e) E is complete (every Cauchy sequence in E converges to a point of E). (f) E is convex.

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3.6.3. Let || · |la and || - ||b be equivalent norms on a vector space X, and
let E be a subset of X. For each of the following statements, prove that the
statement is true with respect to || - ||a if and only if it is true with respect
to || · ||b-
(e) E is complete (every Cauchy sequence in E converges to a point of E).
(f) E is convex.
Transcribed Image Text:3.6.3. Let || · |la and || - ||b be equivalent norms on a vector space X, and let E be a subset of X. For each of the following statements, prove that the statement is true with respect to || - ||a if and only if it is true with respect to || · ||b- (e) E is complete (every Cauchy sequence in E converges to a point of E). (f) E is convex.
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