Convergence structures for categories

Applied Categorical Structures

Volumn 9, Issue 6, 2001, Pages 557-570

  Šlapal, Josef ^a  

^a BRNO UNIVERSITY OF TECHNOLOGY   (Czech Republic)

Author keywords

Closure operator for a category; Convergence and limit structures for a category; Net with respect to a functor; Separation and compactness with respect to a convergence structure

Indexed keywords

EID: 0035508831     PISSN: 09272852     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1012569528842     Document Type: Article

References (19)

1. Adámek, J., Herrlich, H. and Strecker, G. E.: Abstract and Concrete Categories, Wiley, New York, 1990.
2. Čech, E.: Topological Spaces, in Topological Papers of E. Čech, Academia, Prague, 1968, pp. 436-472.
3. Čech, E.: Topological Spaces, Revised by Z. Frolík and M. Katětov, Academia, Prague, 1966.
4. Clementino, M. M., Giuli, E. and Tholen, W.: Topology in a category: Compactness, Portugal. Math. 53 (1996), 397-433.
5. Clementino, M. M. and Tholen, W.: Separation versus connectedness, Topology Appl. 75 (1997), 143-181.
6. Clementino, M. M. and Tholen, W.: Tychonoff's theorem in a category, Proc. Amer. Math. Soc. 124 (1996), 3311-3314.
7. Dikranjan, D. and Giuli, E.: Closure operators I, Topology Appl. 27 (1987), 129-143.
8. Dikranjan, D., Giuli, E. and Tholen, W.: Closure Operators II, in Proc. Int. Conf. on Categorical Topology, Prague 1988, World Scientific, Singapore, 1989, pp. 279-335.
9. Dikranjan, D. and Tholen, W.: Categorical Structure of Closure Operators, Kluwer Acad. Publ., Dordrecht, 1995.
10. Dudley, R. M.: On sequential convergence, Trans. Amer. Math. Soc. 112 (1964), 483-507.
11. Engelking, R.: General Topology, Polish Scientific Publishers, Warszawa, 1977.
12. Kelley, J. L.: General Topology, Van Nostrand, Princeton, 1963.
13. Mac Lane, S.: Categories for the Working Mathematician, Springer-Verlag, New York, 1971.
14. Novák, J.: On some problems concerning multivalued convergences, Czech. Math. J. 14 (1964), 548-561.
15. Preuß, G.: Theory of Topological Structures, D. Reidel Publ. Comp., Dordrecht, 1988.
16. Šlapal, J.: Net spaces in categorical topology, Ann. New York Acad. Sci. 806 (1996), 393-412.
17. Šlapal, J.: Compactness in categories of S-net spaces, Appl. Categorical Structures 6 (1998), 515-525.
18. Spanier, E.: Quasi-topologies, Duke Math. J. 30 (1964), 1-14.
19. Wichterle, K.: On B-convergence spaces, Czechoslovak Math. J. 18 (1968), 569-558.