Baire property of spaces of [0, 1]-valued continuous functions

Abstract

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 for the function space Cp(X, [0 , 1]) to be Baire for a Tychonoff space X all separable closed subsets of which are C∗-embedded. In particular, this characterization holds for normal spaces and, hence, for metrizable spaces. Moreover, we established that the space Cp(X, [0 , 1]) is Baire if and only if Cp(X, K) is Baire for a Peano continuum K. © 2022, The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid.