SOME REMARKS ON M-EMBEDDING

There are four main results in this paper: (1) a necessary condition for the product of a space with any metric space to be normal, (2) a characterization of compact T2 spaces, (3) a complete analogue of the Morita-Hoshina Homotopy Extension Theorem (3.7 [13]) for ANR spaces, and (4) a char acterization of spaces for which every metric space is an AE. Each of these results involves the notion of M-embedding, which was introduced in [17]. (See also [8], [15]) In what follows, Y will denote an infinite cardinal number, R will denote the reals, p the irrationals, and I the unit interval; all functions and pseudometrics will be assumed continuous. No separation axioms will be assumed unless stated. We say a subspace S of a topological space X is MY-em bedded (PY-embedded) in X if every function from S to