Classification of function spaces with the pointwise topology determined by a countable dense set

Abstract

We are concerned with C A (X), the space of continuous real valued functions on X considered with the topology of pointwise convergence on A, where A is a countable dense subset of X. We focus on the Borel and the topological classifications of the spaces C A (X). For example, we prove that for countable nondiscrete X, C A (X) is homeomorphic to , the countable product of = {(x i ) R | x i = 0 a.e.}, provided C A (X) F .