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nLab

cofinite subset

# Contents

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.

Last revised on May 21, 2017 at 16:49:46.
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