Abstract:
For a compact space T it is known that the space Cp(T) (of all continuous functions in T, endowed with the pointwise convergence topology p) is fragmentable by a metric that majorizes p if and only if it is fragmentable by another metric which majorizes the sup-norm topology in C(T). We show that this fact remains valid for pseudocompact spaces T. For pseudocompact and for strongly pseudocompact spaces T we give characterizations of fragmentability of Cp(T) by means of a topological game which is a modification of a game used earlier for characterization of fragmentability. The results are based on a recent generalization of the theorem of Eberlein.
