Exercises (1)1. Let X be any nonempty set and let p€ X, Prove that : E, = {G C X : p¢ G}U{X}is a topology on X.2. Let X be any uncountable set, Prove that: T {GC X : G is countable} U (0} is atopology on X.3. If ACX such that A # 0 and 7 = {GC X: Gn A = 0}U {X} then prove that r is atopology on X. If A = {p}, what is the topology 7 in this case?T%3=

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1. Let X be any nonempty set and let p E X, Prove that : E, {G X:p¢ G}U{X} is a topology on X.

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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Exercises (1)
1. Let X be any nonempty set and let p€ X, Prove that : E, = {G C X : p¢ G}U{X}
is a topology on X.
2. Let X be any uncountable set, Prove that: T {GC X : G is countable} U (0} is a
topology on X.
3. If ACX such that A # 0 and 7 = {GC X: Gn A = 0}U {X} then prove that r is a
topology on X. If A = {p}, what is the topology 7 in this case?
T%3=

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