Cardinal Invariants of the Topology of Uniform Convergence on Compact Sets on the Space of Minimal USCO Maps

Abstract

For a Baire space X the set of all minimal USCO real-valued maps on X coincides with the space D * (X) of locally bounded densely continuous real-valued forms on X. When X is a locally compact space, the space D * k (X) of locally bounded densely continuous real-valued forms on X, under the topology of uniform convergence on compact sets, is a locally convex linear topological space. This paper gives characterizations and bounds for the cardinal function properties on D * k (X) of character, pseudocharacter, density, weight, netweight and cellularity. Examples are given to show how these properties can be the same or different. We answer also some questions posed in