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T0 convergence-approach spaces

Yıl 2020, Cilt: 69 Sayı: 1, 603 - 612, 30.06.2020

Muhammad Qasim Mehmet Baran

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

Öz

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.

Anahtar Kelimeler

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

Destekleyen Kurum

Nil

Proje Numarası

Nil

Teşekkür

Nil

Kaynakça

  • 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.

Yıl 2020, Cilt: 69 Sayı: 1, 603 - 612, 30.06.2020

Muhammad Qasim Mehmet Baran

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

Öz

Proje Numarası

Nil

Kaynakça

  • 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.
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Muhammad Qasim 0000-0001-9485-8072

Mehmet Baran 0000-0001-9802-3718

Proje Numarası Nil
Yayımlanma Tarihi 30 Haziran 2020
Gönderilme Tarihi 23 Ağustos 2019
Kabul Tarihi 8 Ocak 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 69 Sayı: 1

Kaynak Göster

APA 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. Haziran 2020;69(1):603-612. doi:10.31801/cfsuasmas.609919
Chicago Qasim, Muhammad, ve Mehmet Baran. “T0 Convergence-Approach Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, sy. 1 (Haziran 2020): 603-12. https://doi.org/10.31801/cfsuasmas.609919.
EndNote Qasim M, Baran M (01 Haziran 2020) T0 convergence-approach spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 603–612.
IEEE M. Qasim ve M. Baran, “T0 convergence-approach spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 69, sy. 1, ss. 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 (Haziran 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 ve Mehmet Baran. “T0 Convergence-Approach Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 69, sy. 1, 2020, ss. 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.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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