Concerning certain minimal cover refineable spaces

The concept of minimal cover refineable spaces was first used by R. Arens and J. Dugundji. This paper extends their results by showing both additional properties which imply minimal cover refineability and additional properties which are implied by minimal cover refineability. In the course of the research for this paper, some properties of dense subspaces of certain minimal cover refineable spaces were noted. In particular, it was noted that every Nagata space contains a dense metric subspace.