(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED]Finite-Compliment Topology and intersection of interior

1. The problem statement, all variables and given/known data

Given topological space (R[tex]^{1}[/tex], finite compliment topology), find counter example to show that

Arbitary Intersection of (interior of subset of R[tex]^{1}[/tex]) is not equal to Interior of (arbitary intersection of subset of R[tex]^{1}[/tex]).

[tex]\bigcap^{\infty}_{n=1}int(A_{n})\neq int(\bigcap^{\infty}_{n=1}A_{n}) [/tex]

2. Relevant equations

When we consider topological space (R[tex]^{1}[/tex], usual topology), it is easy to find out that [-1/n, 1/n] is the example.

3. The attempt at a solution

First, I thought what shapes the open of topological space (R[tex]^{1}[/tex], finite compliment topology) might have, and it seems to have some shape of real line having finite omissions.

And I tried [tex] A_{n}[/tex] = R-[-1/n, 1/n], and [-1/n, 1/n], but found out all of these are not counterexample..

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# Homework Help: Finite-Compliment Topology and intersection of interior

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