In mathematics, the compact complement topology is a topology defined on the set ${\displaystyle \scriptstyle \mathbb {R} }$ of real numbers, defined by declaring a subset ${\displaystyle \scriptstyle X\subseteq \mathbb {R} }$ open if and only if it is either empty or its complement ${\displaystyle \scriptstyle \mathbb {R} \setminus X}$ is compact in the standard Euclidean topology on ${\displaystyle \scriptstyle \mathbb {R} }$.

References

• Steen, Lynn Arthur; Seebach, J. Arthur Jr. (1995) [1978], Counterexamples in Topology ( Dover reprint of 1978 ed.), Berlin, New York: Springer-Verlag, ISBN  978-0-486-68735-3, MR  0507446

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