The Menger and projective Menger properties of function spaces with the set-open topology

2018/03/20 by Osipov, Alexander V.
#FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1803.07633

Abstract

For a Tychonoff space X and a family λ of subsets of X, we denote by C_λ(X) the space of all real-valued continuous functions on X with the set-open topology. In this paper, we study the Menger and projective Menger properties of a Hausdorff space C_λ(X). Our main results state that if λ is a π-network of X then (1) C_λ(X) is Menger space if and only if it is σ-compact, if Y is a dense subset of X then (2) C_p(Y\vert X) is projective Menger space if and only if it is σ-pseudocompact.

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