Concerning first countable spaces. III

Abstract

The primary purpose of this paper is (1) to provide a “real” example of a regular first countable T 1 {T_1} -space which has no dense developable subspace and (2) to provide a new technique for producing Moore spaces which fail to have dense metrizable subspaces. Related results are established which produce new examples of noncompletable Moore spaces and which show that each regular hereditary M M -space with a G δ {G_\delta } -diagonal has a dense metrizable subspace.