# nLab locally finite cover

### Context

#### Topology

topology

algebraic topology

# Contents

## Idea

A cover which is locally a finite cover.

## Definition

A cover (open cover) $\{U_\alpha\}$ of a topological space $X$ is locally finite if for all $x\in X$, there is an neighbourhood $N \ni x$ such that $N \cap U_\alpha \neq \emptyset$ for only a finite number of $\alpha$.

Open covers defined by partitions of unity are locally finite. (CHECK!)

Revised on July 17, 2014 22:56:06 by Urs Schreiber (82.136.246.44)