Homeomorphisms of function spaces and hereditary cardinal invariants

Abstract

A space X is called a t-image of Y if C-p(X) is homeomorphic to a subspace of C-p(Y). We prove that if Y is a t-image of X, then Y is a countable union of images of X under almost lower semicontinuous finite-valued mappings (see Definition 1.4). It follows that if Y is a t-image of X (in particular, if X and Y are t-equivalent), then for every n is an element of omega, h1(Y-n) less than or equal to h1(X-n),hd(Y-n) less than or equal to hd(X-n) and s(Y-n) less than or equal to s(X-n). (C) 1997 Elsevier Science B.V.