T0 convergence-approach spaces

Year 2020, Volume: 69 Issue: 1, 603 - 612, 30.06.2020

Muhammad Qasim , Mehmet Baran

https://doi.org/10.31801/cfsuasmas.609919

Abstract

In previous papers, several T₀-objects in set-based topological category have been introduced and compared. In this paper, we give the characterization of general T₀ (resp. T₀, and T₀′) convergence approach spaces as well as show how these notions are linked to each other.

Keywords

convergence-approach space, topological category, T0 objects, initial lift, final lift

Supporting Institution

Nil

Project Number

Nil

Thanks

Nil

References

• Adamek, j., Herrlich, H. and Strecker. G. E., Abstract and Concrete Categories, Pure and Applied Mathematics, John Wiley & Sons, New York, 1990.
• Baran, M., Separation properties, Indian J. pure appl. Math, 23 (1991), 333--341.
• Baran, M. and Altindiş, H., T₀ objects in topological categories, J. Univ. Kuwait (Sci.), 22 (1995), 123--127.
• Baran, M., Separation Properties in Topological Categories, Math. Balkanica., 10 (1996), 39--48.
• Baran, M. and Altindiş, H., T₂ objects in Topological Categories, Acta Mathematica Hungarica, 71(1-2) (1996), 41--48.
• Baran, M., Kula, S. and Erciyes, A., T₀ and T₁ semiuniform convergence spaces, Filomat, 27.4 (2013), 537--546.
• Baran, T. M., T₀ and T₁ Pseudo-Quasi-Semi Metric Spaces, Ph.D. Thesis, Erciyes University, 2018.
• Brummer, G. C., A categorical study of initiality in Uniform topology, Ph.D. Thesis, University of Cape Town, 1971.
• Harvey, J., T₀-separation in topological categories, Quaestiones Mathematicae, 2.(1-3) (1977), 1971--1990.
• Hermann, G. T., On topology as applied to image analysis, Computer vision, graphics and Image processing, 52.3 (1990), 409--415.
• Hoffmann, R. E., (E,M)-Universally topological functors, Habilitationsschnift, University of Dusseldorf, 1974.
• Jager, G., A note on neighbourhoods for approach spaces, Hacettepe Journal of Mathematics and Statistics, 41.2 (2012), 283--290.
• Janelidze, G., Light morphisms for generalized T₀-reflections, Topology and its Applications, 156.12 (2009), 2109--2115.
• Kovalevsky, V. A., Finite topology as applied to image analysis, Computer vision, graphics and Image processing, 46.2 (1989), 141--161.
• Kovalevsky, V. A. and Kopperman, R., Some topology-based image processing algorithms, Annals of the New York Academy of Sciences, 728.1 (1994), 174--182.
• Lowen, E. and Lowen, R., Topological quasitopos hulls of categories containing topological and metric objects, Cahiers de topologie et géométrie différentielle catégoriques, 30.3 (1989), 213--228
• Lowen, R., Approach spaces A common Supercategory of TOP and Met, Mathematische Nachrichten, 141.1 (1989), 183--226.
• Lowen, R., Approach spaces: The missing link in the Topology-Uniformity-Metric triad, Oxford University Press, 1997.
• Lowen, R. and Sioen, M., A note on separation in AP, Applied general topology, 4.2 (2003), 475--486.
• Lowen, R., Index Analysis: Approach theory at work, Springer, 2015.
• Marny, T., Rechts-Bikategoriestrukturen in topologischen Kategorien, Ph. D. Thesis, Free University of Berlin, 1973.
• Preuss, G., Theory of topological structures: an approach to categorical topology, D. Reidel Publ. Co., Dordrecht, 1988.
• Preuss, G., Foundations of topology: an approach to convenient topology, Kluwer Academic Publishers, Dordrecht, 2002.
• Salibra, A., A Continuum of theories of lambda calculus without semantics, Proceedings of 16th Annual IEEE Symposium on logic in computer science, 2001.
• Stoy, J. E., Denotational Semantics: The Scott-Strachey approach to programing language, MIT press, 1977.
• Taylor, P., Sober spaces and continuations, Theory and Applications of Categories, 10.12 (2002), 248--300.
• Weck-Schwarz, S., T₀-objects and separated objects in topological categories, Quaestiones Mathematicae, 14.3 (1991), 315--325.