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4. Let X be a non-empty set and p E X be a specific point. Let T = {UC Xpe U} U {0}. Answer each of the following: (i) J is a topology on X. 1

4. Let X be a non-empty set and p E X be a specific point. Let T = {UC Xpe U} U {0}. Answer each of the following: (i) J is a topology on X. 1

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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Question
Please solve 4i,ii,iii
(ii) Let A C X. Identify the closure and interior of A. (iii) Show that the space is To, but not T₁. 5. Consider the function f : (X, T) → (Y, U), where (X, T) and (Y, U) are two topological spaces. Define f to be continuous. Then prove that the following statements are equivalent: (a) f in a continuous function!
Transcribed Image Text:(ii) Let A C X. Identify the closure and interior of A. (iii) Show that the space is To, but not T₁. 5. Consider the function f : (X, T) → (Y, U), where (X, T) and (Y, U) are two topological spaces. Define f to be continuous. Then prove that the following statements are equivalent: (a) f in a continuous function!
4. Let X be a non-empty set and p E X be a specific point. Let T= {U C Xp EU} U {0}. Answer each of the following: (i) J is a topology on X. 1
Transcribed Image Text:4. Let X be a non-empty set and p E X be a specific point. Let T= {U C Xp EU} U {0}. Answer each of the following: (i) J is a topology on X. 1
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