Local T1 Preordered Spaces

Abstract

The aim of this paper is to characterize local T1 preordered spaces as well as to investigate some

invariance properties of them.

Keywords

• Topological category,discrete objects,preorderd spaces

References

1. Adamek, J. , Herrlich, H., Strecker, G.E., Abstract and Concrete Categories, John Wiley and Sons, New York, 1990.
2. Baran, M., {\em Separation properties}, Indian J. Pure Appl. Math., \textbf{23}(1991), 333--341.
3. Baran, M., {\em The notion of closedness in topological categories}, Comment. Math. Univ. Carolinae, \textbf{34}(1993), 383--395.
4. Baran, M., Altindis, H., {\em $T_2$-objects in topological categories}, Acta Math. Hungar. \textbf{71}(1996), 41--48.
5. Baran, M., {\em Separation properties in topological categories}, Math Balkanica \textbf{10}(1996), 39--48.
6. Baran, M., {\em Completely regular objects and normal objects in topological categories}, Acta Math. Hungar., \textbf{80}(1998), 211--224.
7. Baran, M., {\em Closure operators in convergence spaces}, Acta Math. Hungar. \textbf{87}(2000), 33--45.
8. Baran, M., {\em Compactness, perfectness, separation, minimality and closedness with respect to closure operators}, Applied Categorical Structures, \textbf{10}(2002), 403--415.

9. Baran, M., Al-Safar, J., {\em Quotient-Reflective and Bireflective Subcategories of the category of Preordered Sets}, Topology and its Appl., \textbf{158}(2011), 2076--2084.
10. Baran, M. Kula, S., Erciyes, A., {\em $T_0$ and $T_1$ semiuniform convergence space}, Filomat, \textbf{27}(2013), 537--546.
11. Baran, M., Kula, S., Baran, T.M., Qasim, M., {\em Closure operators in semiuniform convergence space}, Filomat, \textbf{30}(2016), 131--140.
12. Baran, T.M., Kula, M., {\em $T_1$ Extended pseudo-quasi-semi metric spaces }, Mathematical Sciences and Appl. E-Notes, \textbf{5}(2017), 40--45.
13. Dikranjan, D., Giuli, E., {\em Closure operators I}, Topology and its Appl., \textbf{27}(1987), 129--143.
14. Dikranjan, D., Tholen, W., Categorical Structure of Closure Operators: with Applications to Topology, Algebra and Discrete Mathematics, Kluwer Academic Publishers, Dordrecht, 1995.
15. Duquenne, V., {\em Latticial structure in data analysis}, Theoret. Comput. Sci. \textbf{217}(1999), 407--436.
16. Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M., Scott, D.S., Continuous Lattices and Domains, Encyclopedia of Mathematics and its Applications, vol. 93, Cambridge University Press, 2003.
17. Kula, M., {\em A note on Cauchy spaces}, Acta Math Hungar., \textbf{133}(2011), 14--32.
18. Koshevoy, G.A., {\em Choice functions and abstract convex geometries}, Math. Social Sci., \textbf{38}(1999), 35--44.
19. Larrecq, J.G., Non-Hausdorff Topology and Domain Theory, Cambridge University Press, 2013.
20. Nel, L.D., {\em Initially structured categories and cartesian closedness}, Canadian J.Math., \textbf{27}(1975), 1361-1377.
21. Preuss, G., Theory of Topological Structures, An Approach to Topological Categories, Dordrecht; D Reidel Publ Co, 1988.
22. Preuss, G., Foundations of topology, An approach to Convenient topology, Kluwer Academic Publishers, Dordrecht, 2002.
23. Scott, D.S., {\em Continuous lattices}, Lecture Notes in Mathematics, Springer-Verlag, \textbf{274}(1972), 97--136.
24. Scott, D.S., {\em Data types as lattices}, Proceedings of the International Summer Institute and Logic Colloquium, Kiel, in: Lecture Notes in Mathematics, Springer-Verlag, \textbf{499}(1975), 579--651.
25. Scott, D.S., {\em Domains for denotational semantics}, in: Lecture Notes in Comp. Sci., Springer-Verlag, \textbf{140}(1982), 97--136.
26. Winskel, G. The Formal Semantics of Programming Languages, an Introduction. Foundations of Computing Series. The MIT Press, 1993.