On selective sequential separability of function spaces with the compact-open topology

Abstract

For a Tychonoff space X, we denote by Ck (X) the space of all real-valued continuous functions on X with the compact-open topology. A subset A ⊂ X is said to be sequentially dense in X if every point of X is the limit of a convergent sequence in A. A space Ck (X) is selectively sequentially separable (in Scheepers’ terminology: Ck (X) satisfies Sfin(S, S)) if whenever (Sn: n ∈ N) is a sequence of sequentially dense subsets of Ck (X), one can pick finite Fn ⊂ Sn (n ∈ N) such that∪ {Fn: n ∈ N} is sequentially dense in Ck (X). In this paper, we give a characterization for Ck (X) to satisfy Sfin(S, S). © 2019, Hacettepe University. All rights reserved.