(adsbygoogle = window.adsbygoogle || []).push({}); Definition of "compactness" in the EXTENDED complex plane?

How does one define a compact set in the extended complex plane [itex]\mathbb C^* = \mathbb C \cup \{ \infty \}[/itex]? "Closed and bounded" doesn't really make sense anymore, as I'm assuming it's permissible for a compact set to contain the point at infinity...right? I guess the "finite subcover" definition still holds, as always, but this doesn't seem very useful. Are there other, more helpful, equivalent characterizations for compact subsets of [itex]\mathbb C^*[/itex]?

**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!

# Definition of compactness in the EXTENDED complex plane?

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