Tychonoff Convergence Spaces
by
Mehmet Baran
Erciyes University, Kayseri-Turkey
Coauthors: Muammer Kula

TYCHONOFF CONVERGENCE SPACES

Mehmet Baran and Muammer Kula
Department of Mathematics, Erciyes University,
Kayseri, 38039 - Turkey
E-mail: baran@erciyes.edu.tr

One of the important classes of topological spaces to deal with is the class of Tychonoff spaces, i.e completely regular T₁ spaces, which is identical with the class of all subspaces of either compact Hausdorff spaces or normal spaces. In particular, there are non-constant continuous functions on every Tychonoff space into the real numbers with the usual topology. Tychonoff spaces are, moreover, the most general topological spaces that can be guaranteed to have this property.

In earlier papers, various generalizations of Tychonoff objects for an arbitrary topological category were defined. Our principal objective in this paper is to characterize each of these objects in the categories of filter and local filter convergence spaces as well as to examine how these various generalizations are related.

References

1. M. Baran and H. Altindis, T2-Objects in Topological Categories, Acta Math. Hungar., 71 (1996), 41-48.

2. M. Baran, A Notion of Compactness in Topological Categories, Publ. Math. Debrecen., 50 (3-4) (1997), 221-234.

3. M. Baran, Completely Regular Objects and Normal Objects in Topological Categories, Acta Math. Hungar., 80 (1998), 211-224.

4. M. Baran, T3 and T4-Objects in Topological Categories, Indian J. Pure Appl. Math., 29 (1998), 59-69.

5. M. M. Clementino, E. Giuli, and W. Tholen, Topology in a Category : Compactness, Portugal. Math., 53 (1996), 397-433.

Date received: June 11, 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-18.