Compactness in Categories of {\cal S}-Net Spaces

Author: lapal J.

Source: Applied Categorical Structures, Volume 6, Number 4, December 1998 , pp. 515-525(11)

Publisher: Springer

Abstract:

The {\cal S}-net spaces studied are convergence structures whose convergences are expressed by using generalized nets, the so called {\cal S}-nets, which are obtained from the usual nets by replacing the category of directed sets and cofinal maps with an arbitrary construct {\cal S}. We investigate compactness in categories of {\cal S}-net spaces defined by introducing continuous maps in a natural way and imposing some usual convergence axioms.

Keywords: convergence -net space; limit -net space; compact -net space; rectangular -net space; Cartesian closed category

Language: English

Document Type: Regular paper

Affiliations: 1: Department of Mathematics, Technical University of Brno, Technická 2, 61669 Brno, Czech Republic. e-mail: Email: slapal@kinf.fme.vutbr.cz

Publication date: 1998-12-01

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