الفئات المحكمة

Abstract

For any locally convex space E, the bounded set D is precompact if and only if linm (sn(D,U))=0 for any nhood of zero in E. In this work we study some type of precompact (which are called - compact) sets whose sequences of n-diameters converges to zero in different rates (rapidly, radically,…), and we prove that the Cartesian product of infinite - compact sets (operators) are - compact. Also compact (where G (akn) is any stable nuclear kothe space under some conditions) if and only if H BE and H BF are