Material :Daly analysis

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Material :Daly analysis
2.8.21. The closed unit disk in l is D = {x E l: ||x||1 < 1}. Give direct
proofs of the following statements.
(a) D is a closed and bounded subset of l.
(b) D is not sequentially compact.
(c) D is not totally bounded.
(d) The collection of open balls {B2(±8n)}nEN Covers D but does not have
a finite subcover, so D is not compact.
Transcribed Image Text:2.8.21. The closed unit disk in l is D = {x E l: ||x||1 < 1}. Give direct proofs of the following statements. (a) D is a closed and bounded subset of l. (b) D is not sequentially compact. (c) D is not totally bounded. (d) The collection of open balls {B2(±8n)}nEN Covers D but does not have a finite subcover, so D is not compact.
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