On j_{1, 2}-countable compactness and filters
by
T. Hatice Yalvac
Hacettepe University, Ankara

In an earlier work [17] we have defined j_{1, 2}-countable compact spaces and j_{1, 2}-countable compact sets relative to a space, and used these to unify various concepts in this area. By giving some new relations concerning j_{1, 2}-countable compactness, filters and j_{1, 2}-closure, we continue this process of unification.

References

1. Abd El-Monsef, M. E. and Lashien, E. F., Local discrete extensions of supratopologies, Tamkong J. Math 31, No. 1, 1990, 1-6.
2. Dickmann, R. F. Jr. and Porter J. R., \theta-perfect and absolutely closed functions, Illinois J. Math., 21, 1977, 42-60.
3. Dickmann, R. F. Jr. and Krystock, R. L., S-sets and S-perfect mappings, Proc. Amer. Math. Soc. 80(4), 1980, 687-692.
4. Di Maio, G. and Noiri, T., On s-closed spaces, Indian J.Pure Appl. Math., 18(3), 1987, 226-233.
5. Dlaska, K. and Ergun, N., Ganster, M., Countably S-closed spaces, Math. Slovaca, 44, No 3, 1994, 337-348.
6. Dontchev, J., Ganster, M., On covering spaces with semi-regular sets, Ricerche Math. 45, 1996, 229-245.
7. Herrmann, R.A., 1979, RC-convergence, Proc. Amer. Math. Soc., 75, 2, 1979, 311-317.
8. Herrington, L.L. and Long, P.E., 1975, Chracterizations of H-closed spaces, Proc. Amer. Math. Soc., 48, 2, 1975, 469-475.
9. Kandil, A., Kerre, E. E. and Nouh, A. A., Operations and mappings on fuzzy topological spaces, Ann. Soc. Sci. Bruxelles, 105, No 4, 1991, 165-168.
10. Maheshwari, S. N. and Thakur, S. S., 1981, Jour. Sci. Res., 3, 121-123.
11. Maheshwari, S. N. and Thakur, S. S., On \alpha-compact spaces, Bulletin of the Institute of Mathematics Academia Sinica 13 (4), 1985, 341-347.
12. Noiri, T., On RS-compact spaces, J. Korean Math. Soc., 22, No 1, 1985, 19-34.
13. Raghavan, T. G., On H(1)-closed spaces-II, Bull. Col. Math. Soc., 77, 1985, 171-180.
14. Stephenson, R. M. JR., Pseudocompact spaces, Trans. Amer. Math. Soc. 134, 1968, 437-448.
15. Tranapalan, D. P. T. and Raghavan, T. G., On strongly H(1)-closed spaces, Bull. Cal. Math. Soc., 76, 1984, 370-383.
16. Yalvaç, T. H., A unified approach to compactness and filters, Hacettepe Bull. Math. Sci. Eng., Series B, 29, 2000, 63-75.
17. Yalvaç, T. H., 2000, On some unifications, The first Turkish International Conference on Topology and its Applications, submitted.

Date received: July 17, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagx-42.