Let $X$ be a topological space.
Assuming the axiom of choice then the following are equivalent:
$X$ is a fully normal topological space;
$X$ 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.
Last revised on May 23, 2017 at 04:49:52. See the history of this page for a list of all contributions to it.