Compactoid filters and USCO maps

The aim of this paper is to report in a short and self-contained way on the properties of compactoid and countably compactoid filters. We apply them to some questions in both topology and analysis such as the generation and extension of USCO maps, the study of some properties of K-analytic spaces and the study of bounds for the weight of compact sets in spaces obtained through inductive operations.  2003 Elsevier Inc. All rights reserved