Let (X, τ1) be any topological space and (X, τf ) be the finite complement topological space.Show that the space (X, τ1) is a T1−space if and only if τf ⊆ τ1. 2. Let (X, 1) be any topological space and (X, Tf) be the finite complement topological space.Show that the space (X, 71) is a T1-space if and only if Tf C T1.

Answered: 2. Let (X, 1) be any topological space…

2. Let (X, 1) be any topological space and (X, Tf) be the finite complement topological space. Show that the space (X,71) is a T1- space if and only if Tf C TI.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 24CM

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Question

Let (X, τ1) be any topological space and (X, τf ) be the finite complement topological space.
Show that the space (X, τ1) is a T1−space if and only if τf ⊆ τ1.

2. Let (X, 1) be any topological space and (X, Tf) be the finite complement topological space.
Show that the space (X, 71) is a T1-space if and only if Tf C T1.

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