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In [[mathematics]], the '''compact complement topology''' is a [[topological space|topology]] defined on the set <math>\scriptstyle\mathbb{R}</math> of [[real numbers]], defined by declaring a [[subset]] <math>\scriptstyle X \subseteq \mathbb{R}</math> [[open set|open]] [[if and only if]] it is either empty or its [[complement (set theory)|complement]] <math>\scriptstyle\mathbb{R} \setminus X</math> is compact in the standard [[Euclidean space|Euclidean topology]] on <math>\scriptstyle\mathbb{R}</math>.

==References==
*{{Citation | last1=Steen | first1=Lynn Arthur | author1-link=Lynn Arthur Steen | last2=Seebach | first2=J. Arthur Jr. | author2-link=J. Arthur Seebach, Jr. | title=[[Counterexamples in Topology]] | orig-date=1978 | publisher=[[Springer-Verlag]] | location=Berlin, New York | edition=[[Dover Publications|Dover]] reprint of 1978 | isbn=978-0-486-68735-3 | mr=507446 | year=1995}}

[[Category:Topology]]

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Compact complement topology - Revision history

imported>Citation bot: Misc citation tidying. | Use this bot. Report bugs. | Suggested by GreysonMB | Category:Topology | #UCB_Category 67/265