# Contents

## Statement

Let $X$ be a topological space.

Assuming the axiom of choice then the following are equivalent:

1. $X$ is a fully normal topological space;

2. $X$ is a paracompact topological space

(Stone 48)

Since metric spaces are fully normal it follows as a corollary that metric spaces are paracompact. Accordingly, this statement is now also known as Stone’s theorem.

## References

• A. H. Stone, Paracompactness and product spaces, Bull. Amer. Math. Soc. Volume 54, Number 10 (1948), 977-982. (Euclid)

Last revised on May 23, 2017 at 04:49:52. See the history of this page for a list of all contributions to it.