(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

E is a compact set, F is a closed set. Prove that intersection of E and F is compact

2. Relevant equations

3. The attempt at a solution

On Hausdoff space (the most general space I can work this out), compact set is closed. So E is closed. So intersection of E and F is closed. That is a closed subset of compact set E so intersection of E and F is closed.

My problem is i can't generalize the proof to general topological space. If E is not in Hausdoff space, it is not necessarily closed. I don't know if I was going in the right direction or not. Please help me with it. Thank you very much.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: About compactness in topology

**Physics Forums | Science Articles, Homework Help, Discussion**