On EM-spaces

Abstract

A Tychonoff space is an EM-space if every bounded continuous function on a cozeroset has a continuous extension on a dense cozeroset. EM-spaces can be considered to generalize F-spaces. In fact a space X is an F-space if and only if it is quasi F-space and EM-space. This generalization contains cozero complemented spaces. We say that a space X has property-I if whenever U∈Coz(X) there are two disjoint cozerosets V1,V2 in X such that ∂U‾⊆∂V1∩∂V2. We prove that a Tychonoff space is cozero complemented if and only if it is an EM-space and has property-I if and only if it is weakly cozero complemented and has property-I. We give answers to many essential questions that concern continuous images of EM-spaces, subspaces and products of EM-spaces.