PRETOPOLOJİK UZAYLAR KATEGORİSİNDE ∂ -BAĞLANTILILIK

Bu çalışmada, verilen herhangi bir ε topolojik kategorisi ve ε nun herhangi bir Χ objesi için, ∂ -bağlantılılık kavramı tanımlanarak bu kavram, Pretopolojik Uzaylar kategorisinde incelenmiştir.

Anahtar Kelimeler:

Bağlantılılık, Topolojik kategori, Yakınsak süzgeç Uzaylar, Pretopolojik uzaylar

A NOTION OF ∂ -CONNECTEDNESS IN THE CATEGORY OF PRETOPOLOGICAL SPACES

In this study, the notion of ∂ -connectedness is defined for any given X object of ε, which is a topological category over sets, and this notion is characterized in the category of pretopological spaces.

Keywords:

Connectedness, Topological category, Convergence space, Pretopological space,

PDF

___

Munkres, J.R., Topology: A First Course, Prentice Hall Inc., New Jersey, 1975.
Baran, M., The Notion of Closedness in Topological Categories, Comment. Math. Univ. Carolinae, 34, 383-395, 1993.
Herrlich, H., Topological Functors, Gen. Top. Appl., 4, 125-142, 1975.
Brümmer, G.C.L., A Categorical Study of Initialy in Uniform Topology, Ph.D. Thesis, Univ. of Cape Town, 1971.
Mielke, M.V., Geometric Topological Completions with Universal Final Lifts, Top. and Appl., 9, 277-293, 1985.
Schwartz, F., Connections Beetween Convergence and Nearness, Lecture Notes in Math. No.719, Springer-Verlag, 345-354, 1978.
Baran, M., Closure Operators in Convergence Spaces, Acta. Math. Hunger., 87, 33-45, 2000.
Baran, M. and Kula, M., A note on Separation and Compactness in Categories of Convergence Spaces, Applied General Topology, 4, 1-13, 2003.
Kula, M., Topolojik Kategorilerde Bağlantılılık, Doktora Tezi, Erciyes Üniversitesi, Kayseri, 2003.
Clementino, M. M. and Tholen, W., Separation Versus Connectedness, Topology and its Applications, 75, 143- 181, 1997.
Collins, P.J., Concordant Mappings and the Concordant-Dissonant Factorization of an Arbitrary Continous Function, Proceedings of the A.M.S, 27, 587-591, 1971.
Dikranjan, D. and Giuli, E., Closure operators I, Topology Appl., 27, 129-143, 1987.
Baran, M., Separation Properties, Indian J. Pure and Appl. Math., 23 (5), 333-341, 1992.