title: Compact complement topology
text: # 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 $\scriptstyle \mathbb {R}$.
  
  