Compact complement topology

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

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 507446