nLab cofinite subset

There are two notions: cofinite subset of a set and a cofinite subset of a (pre)ordered set.

Definition

Given a set $X$, then a subset $S \subset X$ is called cofinite if the complement $X \backslash S$ is a finite set.

A preordered set $(\Lambda,\leq)$ is cofinite or closure finite if for every $\lambda\in\Lambda$ the set of all predecessors of $\lambda$ is finite.

Related concepts

• cofinite topology