2. Let X = {a,b,c,d} and T ={ø.{a},{b},{a,b},{a,b,d},{a,b,c},X}.a) Show that T is a topology on X.b) What are the closed sets in T?%3Dc) What are the closures and interiors of {a} and {b}?d) Determine of the closure of {a,c}.

Answered: Image /qna-images/answer/84d7feab-6996-4683-b8b3-1c4f411e55ef.jpg

Answered: 2. Let X = {a,b,c,d} and T =…

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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This is under Topology class:Answer thisa.) Show that if A is closed in Y and Y is closed in X, then A is closed in X.
A.) Let A be a subset of X, and B be a subset of X, where X is a metric space. Show the intersection of (A and B) complement is a subset of A complement intersection B complement. B.) Consider A =[3,7), B = (7,9] as a subset of R with the usual metric dR(x,y) = abs(x-y). Show A complement intersection B complement is not a subset of the intersection of (A and B) complement.
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2. Let X = {a,b,c,d} and T = {ø,{a},{b},{a,b},{a,b,d},{a,b,c}, X}. a) Show that T is a topology on X. b) What are the closed sets in T? %3D %3D c) What are the closures and interiors of {a} and {b} ? d) Determine of the closure of {a,c}.