Completeness properties for convergence spaces

Eva Lowen-Colebunders

Vol. 70 (1977), No. 2, 401–411

DOI: 10.2140/pjm.1977.70.401

Abstract

For uniform convergence spaces a completeness concept has been introduced by Cook and Fisher. For a uniformizable convergence space it is of interest whether among the uniform convergence structures inducing the given structure, one can find a complete one. Keller has shown that this is the case for every Hausdorff convergence space. Our aim is to introduce a stronger completeness concept. We have developed a theory in which completeness is a generalization of topological completeness for metrizable spaces.

Mathematical Subject Classification 2000

Primary: 54A20

Milestones

Received: 25 October 1976

Revised: 21 February 1977

Published: 1 June 1977