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Topology Q3&4 pls

Topology Q3&4 pls

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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Topology Q3&4 pls
A is closed True or False: B is closed pts True or False: A is a nhood of 0 True or False: B is a nhood of 0 3. Consider the topological space (X, T) where X = R and T = {X, [0, 1], 0}. Let A = {1}. ) List all closed sets in (X, T). Prove cl(A) = R. s.) Prove int(A) = 0. 4. Let (X, d) be the pseudometric space where X = R and d is the usual pseudometric. Let A = = {1/n: n=1,2,...}. Prove that 1 A'. Prove that 0 € A'. 1 co the However, Ho t is just is also e 12. closure Conside and ols
Transcribed Image Text:A is closed True or False: B is closed pts True or False: A is a nhood of 0 True or False: B is a nhood of 0 3. Consider the topological space (X, T) where X = R and T = {X, [0, 1], 0}. Let A = {1}. ) List all closed sets in (X, T). Prove cl(A) = R. s.) Prove int(A) = 0. 4. Let (X, d) be the pseudometric space where X = R and d is the usual pseudometric. Let A = = {1/n: n=1,2,...}. Prove that 1 A'. Prove that 0 € A'. 1 co the However, Ho t is just is also e 12. closure Conside and ols
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