Compact complement topology
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In mathematics, the compact complement topology is a topology defined on the set [math]\displaystyle{ \scriptstyle\mathbb{R} }[/math] of real numbers, defined by declaring a subset [math]\displaystyle{ \scriptstyle X \subseteq \mathbb{R} }[/math] open if and only if it is either empty or its complement [math]\displaystyle{ \scriptstyle\mathbb{R} \setminus X }[/math] is compact in the standard Euclidean topology on [math]\displaystyle{ \scriptstyle\mathbb{R} }[/math].
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
![]() | Original source: https://en.wikipedia.org/wiki/Compact complement topology.
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