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. Prove or disprove every metric space is normed space,

. Prove or disprove every metric space is normed space,

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 (3) 1. Let A be a subset of normed space X. show that [A] is smallest closed subspace of X contain A. 2. Let M be closed subspace of normed space X. Show that M #X iff int(M)= 6 3. Prove or disprove every metric space is normed space, 4. Let A be an open set in a normed space X. Show that A+ B is also open set in X for any subset B of X.
Transcribed Image Text:Exercise (3) 1. Let A be a subset of normed space X. show that [A] is smallest closed subspace of X contain A. 2. Let M be closed subspace of normed space X. Show that M #X iff int(M)= 6 3. Prove or disprove every metric space is normed space, 4. Let A be an open set in a normed space X. Show that A+ B is also open set in X for any subset B of X.
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