Answered: Let X be infinite set and x0 ∈ X.…

Let X be infinite set and x0 ∈ X. Consider the topology τ = {G ⊆ X : x0 ∈ G or G = ∅} on X. Is (X, τ ) compact. Explain why?

Elements Of Modern Algebra

8th Edition

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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Let X be infinite set and x0 ∈ X. Consider the topology τ = {G ⊆ X : x0 ∈
G or G = ∅} on X. Is (X, τ ) compact. Explain why?

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