Compact complement topology

From HandWiki

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].

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