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

A topological space X is Baire if the intersection of any sequence open dense subsets in X. Let $$C_p(X,[0,1])$$ denote all continuous [0, 1]-valued functions on a Tychonoff with topology pointwise convergence. In this paper, we have obtained characterization for function to be separable closed which are $$C^*$$ -embedded. particular, holds normal spaces and, hence, metrizable spaces. Moreover, established that and only $$C_p(X,\mathbb {K})$$ Peano continuum $$\mathbb {K}$$ .