2022/03/11 by Alexander V. Osipov, Osipov, Alexander V., Е. Г. Пыткеев +1
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.2203.05976
openalex publication_date 2022/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A topological space X is Baire if the intersection of any sequence of open dense subsets of X is dense in X. Let Cp(X,[0,1]) denote the space of all continuous [0,1]-valued functions on a Tychonoff space X with the topology of pointwise convergence. In this paper, we have obtained a characterization when the function space Cp(X,[0,1]) is Baire for a Tychonoff space X all separable closed subsets of which are C-embedded. In particular, this characterization is true for normal spaces and, hence, for metrizable spaces. Moreover, we obtained that the space Cp(X,[0,1]) is Baire, if and only if, the space Cp(X,K) is Baire for a Peano continuum K.