# 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 $\alpha$.

Any open cover defined by a (generalized) partition of unity has a locally finite shrinking.

Revised on March 17, 2015 21:28:52 by Anonymous Coward (178.203.172.141)