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…

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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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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