Fragmentability of function spaces \(C_p(T)\) for pseudocompact spaces \(T\) (Q2829917)

Let \(T\) be a topological space, and \(C_{p}(T)\) be the set of all continuous real-valued functions on \(T\) endowed with \(p\), the topology of pointwise convergence. It is known that the space \(T\) is fragmentable if and only if the Player II has a winning strategy in the fragmenting game \(G(T)\). In this paper, the authors give a modification of the game \(G\) denoted by \(G'\). They prove, in particular, that if \(T\) is pseudocompact then \(C_p(T)\) is fragmentable by a metric majorizing the topology \(p\) if and only if \(C_p(T)\) is fragmentable by a metric majorizing the norm topology on \(C(T)\) if and only if the Player II has a winning strategy in the game \(G'(C_p(T))\).