The strict topology and compactness in the space of measures. II

摘要: The strict topology : on C(S), the bounded continuous complex valued functions locally compact Hausdorff space S, was first introduced by R. C. Buck [3], [4], [5]. It has also been studied I. Glicksberg [10], J. Wells [20], and Todd [17]. This used in study of various problems spectral synthesis [11], spaces holomorphic [15], multipliers Banach algebras [18], [19]. paper is a detailed account results announced author [6], [7] relationship C(S),B with its dual M(S), Radon measures S. In particular, we are concerned question (posed Buck) whether or not Mackey and, consequently, compactness criteria M(S). existence description topology, strongest yielding given adjoint space, known, there several properties (e.g., metrizable) which imply that designated topology. However, knows no example topological vector an intrinsically defined except virtue some formally stronger property metrizable, barrelled, bornological). true for C(S),B. fact, show if S paracompact then every :-weak* countably subset M(S) /-equicontinuous; (Theorem 2.6). Also, bornological, nor metrizable. can happen as case when ordinal numbers less than uncountable ordinal. ?3 examine subspace problem That is, subspaces C(S) furnished relative topology? We able to solve this positive integers. H O, open unit disk D, endowed topology-even though C(D), is. From these prove closed N 11 such projection onto N. Finally, (1V, O) semireflexive space.