Collectionwise normal and Moore implies metrizable

History
This statement was proved by Moore.

Statement
The statement has the following equivalent forms:


 * 1) If a topological space is both collectionwise normal and a uses property satisfactin of::Moore space, then it is a proves property satisfaction of::metrizable space.
 * 2) If a topological space is both collectionwise normal and a uses property satisfaction of::developable space, then it is a metrizable space.

Note that the converse is easily seen to be true: metrizable implies Moore and metrizable implies collectionwise normal. Thus, the above give necessary and sufficient conditions for a topological space to be metrizable.