Abstract
The \(S\)-net spaces studied are convergence structures whose convergences are expressed by using generalized nets, the so called\(S\)-nets, which are obtained from the usual nets by replacing the category of directed sets and cofinal maps with an arbitrary construct \(S\). We investigate compactness in categories of\(S\)-net spaces defined by introducing continuous maps in a natural way and imposing some usual convergence axioms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adámek, J., Herrlich, H. and Strecker, G. E.: Abstract and Concrete Categories, Wiley, New York, 1990.
Clementino, M. M., Giuli, E. and Tholen, W.: Topology in a category: Compactness, Portugal. Math. 53 (1996), 397–433.
Clifford, A. H. and Preston, G. B.: The Algebraic Theory of Semigroups, Providence, RI, 1964.
Dikranjan, D. and Giuli, E.: Compactness, minimality and closedness with respect to a closure operator, in Categorical Topology and Its Relations to Analysis, Algebra and Combinatorics, Prague 1988, World Scientific, Singapore, 1989, pp. 284–296.
Dikranjan, D. and Tholen, W.: Categorical Structure of Closure Operator, Kluwer Academic Publishers, Dordrecht, 1995.
Edgar, G. A.: A Cartesian closed category for topology, Gen. Topol. Appl. 6 (1976), 65–72.
Engelking, R.: General Topology, Heldermann Verlag, Berlin, 1989.
Plonka, J.: Diagonal algebras, Fund. Math. 58 (1966), 309–321.
Preuss, G.: Theory of Topological Structures, Reidel, Dordrecht, 1988.
Šlapal, J.: Net spaces in categorical topology, Ann. New York Acad. Sci. 806 (1996), 393–412.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Šlapal, J. Compactness in Categories of \(S\)-Net Spaces. Applied Categorical Structures 6, 515–525 (1998). https://doi.org/10.1023/A:1008618211222
Issue Date:
DOI: https://doi.org/10.1023/A:1008618211222