Concerning normality, metrizability and the Souslin property in subspaces of Moore spaces

Abstract

In this paper, the author generalizes the known results concerning the existence of dense metrizable subspaces in normal Moore spaces and characterizes those Moore spaces which have certain types of dense metrizable subspaces. An example is given of a Moore space which has a dense metrizable subspace but for which there exists no development satisfying Axiom C at each point of a dense subset. The concepts developed are also used to investigate various problems related to the normal Moore space conjecture of F.B. Jones and to characterize the Souslin property in Moore spaces.