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.
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.
Year 2020,
Volume: 69 Issue: 1, 603 - 612, 30.06.2020
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.
Qasim, M., & Baran, M. (2020). T0 convergence-approach spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 603-612. https://doi.org/10.31801/cfsuasmas.609919
AMA
Qasim M, Baran M. T0 convergence-approach spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):603-612. doi:10.31801/cfsuasmas.609919
Chicago
Qasim, Muhammad, and Mehmet Baran. “T0 Convergence-Approach Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 603-12. https://doi.org/10.31801/cfsuasmas.609919.
EndNote
Qasim M, Baran M (June 1, 2020) T0 convergence-approach spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 603–612.
IEEE
M. Qasim and M. Baran, “T0 convergence-approach spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 603–612, 2020, doi: 10.31801/cfsuasmas.609919.
ISNAD
Qasim, Muhammad - Baran, Mehmet. “T0 Convergence-Approach Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 603-612. https://doi.org/10.31801/cfsuasmas.609919.
JAMA
Qasim M, Baran M. T0 convergence-approach spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:603–612.
MLA
Qasim, Muhammad and Mehmet Baran. “T0 Convergence-Approach Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 603-12, doi:10.31801/cfsuasmas.609919.
Vancouver
Qasim M, Baran M. T0 convergence-approach spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):603-12.