THE KATETOV-MORITA THEOREM FOR THE DIMENSION OF METRIC FRAMES

The results which appear here are devoted to the dimension theory of metric frames. We begin by characterizing the covering dimension dim of metric frames in terms of special sequences of covers and then prove the fundamental Katetov-Morita Theorem asserting that Ind L = dim L for every metric frame L. Next, we establish two characterizations of the dimension function Ind in Metric frames, one in terms of special bases and another in terms of decompositions into subspaces of dimension zero. These characterizations yield a sum theorem.