SIGMA-FRAGMENTABILITY AND ANALYTICITY

We present a new characterization of sigma-fragmentability and illustr ate its usefulness by proving some results relating analyticity and si gma-fragmentability. We show, for instance, that a Banach space with t he weak topology is sigma-fragmented if, and only if, it is almost Cec h-analytic and that an almost Cech-analytic topological space is sigma -fragmented by a lower-semicontinuous metric if, and only if, each com pact subset of the space is fragmented by the metric.