COVER-STRICT TOPOLOGIES, IDEALS, AND QUOTIENTS FOR SOME SPACES OF VECTOR-VALUED FUNCTIONS

Let X be a completely regular Hausdorff space, let D be a cover of X, and let it pi : epsilon -> X be a bundle of Banach spaces (algebras). Let Gamma(pi) be the space of sections of pi, and let Gamma(b)(pi,D) be the subspace of Gamma(pi) consisting of sections which are bounded on each D is an element of D. We study the subspace (ideal) and quotient structures of some spaces of vector-valued functions which arise from endowing Gamma(b)(pi,D) with the cover-strict topology.