Let X=R and S be the set of irrational numbers. Find the closure of S in the following topologies for R. The topology of the accounting complement

drzwiczkih5a

drzwiczkih5a

Answered question

2022-11-14

Let X = R and S be the set of irrational numbers. Find the closure of S in the following topologies for R
The topology of the accounting complement

Answer & Explanation

Kalmukujobvg

Kalmukujobvg

Beginner2022-11-15Added 14 answers

We need to find the closure of the irrational numbers S in the cocountable topology. That is, we must find the smallest closed set containing the irrational numbers. A set is closed in the cocountable topology iff it is countable or is the whole space. Since S is uncountable, it cannot be contained by any countable set. Therefore its closure is the whole space R .

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?