Compact complement topology

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 ${\displaystyle \scriptstyle \mathbb {R} }$.

• 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