(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]?

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# Definition of compactness in the EXTENDED complex plane?

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