Extending Maps from Products

Abstract

If C be a compact, Hausdorff space and M be a metric space and if C × M ×Y is normal and Z is the image of Y under a closed map, then C × M × Z is normal. This chapter presents an answer to whether X × Z is normal if X is a closed subset of C × M where C is a compact, Hausdorff space and M is a metric space and if X × Y is normal and Z is the image of Y under a closed map. The question is interesting because the class of spaces that can be embedded as a closed subset of a product of a compact, Hausdorff space with a metric space is the class of paracompact p-spaces, also called paracompact M-spaces, which have been studied extensively.