According to definition, a compact set is one where every open cover has a finite sub-cover.(adsbygoogle = window.adsbygoogle || []).push({});

So let say I have C1, which is an open cover, I have C2 subset of C1 which is also an open cover. But C2 is finite.

But since C2 is an open cover then there is a finite subcover C3 which is subset of C2.

And so on and so forth , we will definitely end up with Cz which may only have one element. Then there will be no more subset of Cz, then how can there be any more subcover?

Isn't there a contradiction?

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

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!

# What is a compact space?

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