International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 5, Pages 303-315
doi:10.1155/S0161171201004264
An Ascoli theorem for sequential spaces
Vrije Universiteit Brussel, Department Wiskunde, Pleinlaan 2, Brussel B-1050, Belgium
Received 10 November 1999; Revised 27 December 1999
Copyright © 2001 Gert Sonck. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Ascoli theorems characterize “precompact” subsets of the set of morphisms between two objects of a category in terms of “equicontinuity” and “pointwise precompactness,” with appropriate definitions of precompactness and equicontinuity in the studied category. An Ascoli theorem is presented for sets of continuous functions from a sequential space to a uniform space. In our development we make extensive use of the natural function space structure for sequential spaces induced by continuous convergence and define appropriate concepts of equicontinuity for sequential spaces. We apply our theorem in the context of C*-algebras.