2. Let X be any uncountable set, Prove that : 7. = {GCX: 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 r in this case?

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2. Let X be any uncountable set, Prove that: 7. = (GC X: G is countable} U {0} is a topology on X.

Elements Of Modern Algebra

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ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.3: Properties Of Composite Mappings (optional)

Problem 8E: Suppose f,g and h are all mappings of a set A into itself. a. Prove that if g is onto and fg=hg,...

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2. Let X be any uncountable set, Prove that : 7. = {GCX: 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 r in this case?

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