Araştırma Makalesi
BibTex RIS Kaynak Göster

T₁ Approach Spaces

Yıl 2019, Cilt: 68 Sayı: 1, 784 - 800, 01.02.2019

Mehmet Baran Muhammad Qasım

https://doi.org/10.31801/cfsuasmas.478632
Cited By: 3

Öz

In this paper, we characterize both T₁ and local T₁ limit (resp. gauge) approach spaces as well as show how these concepts are related to each other. Finally, we compare these T₁ and the usual T₁ approach spaces.

Anahtar Kelimeler

Topological category T₁ objects initial lift limit-approach space

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., Separation Properties in Topological Categories, Math. Balkanica, 10 (1996), 39-48.
  • Baran, M., T₃ and T₄-objects in topological categories, Indian J. pure appl. Math., 29 (1998), 59-70. BaranNormal : Baran, M., Completely regular objects and normal objects in topological categories, Acta Mathematica Hungarica, 80.3 (1998), 211-224.
  • Baran, M., Closure operators in convergence spaces, Acta Mathematica Hungarica, 87.1-2 (2000), 33-45.
  • Baran, M. and Al-Safar, J., Quotient-reflective and bireflective subcategories of the category of preordered sets, Topology and its Applications, 158.15 (2011), 2076-2084.
  • Baran, M., Kula, S. and Erciyes, A., T₀ and T₁ semiuniform convergence spaces, Filomat, 27.4 (2013), 537-546.
  • Baran, M., Kula, S., Baran, T. M. and Qasim, M., Closure Operators in Semiuniform Convergence Spaces, Filomat 30.1 (2016), 131-140.
  • Baran, M. and Qasim, M., Local T₁ Distance-Approach Spaces, Proceedings of 5th International Conference on Advanced Technology & Sciences (ICAT), Bahcesehir University, Istanbul, Turkey, (2017), 112-116.
  • Baran, T.M. and Kula, M., T₁ Extended Pseudo-Quasi-Semi Metric Spaces, Math. Sci. Appl. E-Notes, 5.1 (2017), 40-45.
  • Berckmoes, B., Lowen, R. and Van Casteren, J., Approach theory meets probability theory, Topology and its Applications, 158.7 (2011), 836-852.
  • Colebunders, E., De Wachter S., and Lowen R., Intrinsic approach spaces on domains, Topology and its Applications, 158.17 (2011), 2343-2355.
  • Dikranjan, D. and Giuli, E., Closure operators I, Topology and its Applications, 27.2 (1987), 129-143.
  • Dikranjan, D. and Tholen, W., Categorical structure of closure operators: with applications to topology, algebra and discrete mathematics, Kluwer Academic Publishers, Dordrecht, 1995.
  • Jager, G., A note on neighbourhoods for approach spaces, Hacettepe Journal of Mathematics and Statistics, 41.2 (2012), 283-290.
  • 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 Windels, B., Approach groups, The Rocky Mountain Journal of Mathematics, 30 (2000), 1057-1073.
  • Lowen, R. and Sioen, M., A note on separation in AP, Applied general topology, 4.2 (2003), 475-486.
  • Lowen, R., and Verwulgen, S., Approach vector spaces, Houston J. Math , 30.4 (2004), 1127-1142.
  • Lowen, R., Index Analysis: Approach theory at work, Springer, 2015.
  • 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.

Yıl 2019, Cilt: 68 Sayı: 1, 784 - 800, 01.02.2019

Mehmet Baran Muhammad Qasım

https://doi.org/10.31801/cfsuasmas.478632
Cited By: 3

Öz

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., Separation Properties in Topological Categories, Math. Balkanica, 10 (1996), 39-48.
  • Baran, M., T₃ and T₄-objects in topological categories, Indian J. pure appl. Math., 29 (1998), 59-70. BaranNormal : Baran, M., Completely regular objects and normal objects in topological categories, Acta Mathematica Hungarica, 80.3 (1998), 211-224.
  • Baran, M., Closure operators in convergence spaces, Acta Mathematica Hungarica, 87.1-2 (2000), 33-45.
  • Baran, M. and Al-Safar, J., Quotient-reflective and bireflective subcategories of the category of preordered sets, Topology and its Applications, 158.15 (2011), 2076-2084.
  • Baran, M., Kula, S. and Erciyes, A., T₀ and T₁ semiuniform convergence spaces, Filomat, 27.4 (2013), 537-546.
  • Baran, M., Kula, S., Baran, T. M. and Qasim, M., Closure Operators in Semiuniform Convergence Spaces, Filomat 30.1 (2016), 131-140.
  • Baran, M. and Qasim, M., Local T₁ Distance-Approach Spaces, Proceedings of 5th International Conference on Advanced Technology & Sciences (ICAT), Bahcesehir University, Istanbul, Turkey, (2017), 112-116.
  • Baran, T.M. and Kula, M., T₁ Extended Pseudo-Quasi-Semi Metric Spaces, Math. Sci. Appl. E-Notes, 5.1 (2017), 40-45.
  • Berckmoes, B., Lowen, R. and Van Casteren, J., Approach theory meets probability theory, Topology and its Applications, 158.7 (2011), 836-852.
  • Colebunders, E., De Wachter S., and Lowen R., Intrinsic approach spaces on domains, Topology and its Applications, 158.17 (2011), 2343-2355.
  • Dikranjan, D. and Giuli, E., Closure operators I, Topology and its Applications, 27.2 (1987), 129-143.
  • Dikranjan, D. and Tholen, W., Categorical structure of closure operators: with applications to topology, algebra and discrete mathematics, Kluwer Academic Publishers, Dordrecht, 1995.
  • Jager, G., A note on neighbourhoods for approach spaces, Hacettepe Journal of Mathematics and Statistics, 41.2 (2012), 283-290.
  • 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 Windels, B., Approach groups, The Rocky Mountain Journal of Mathematics, 30 (2000), 1057-1073.
  • Lowen, R. and Sioen, M., A note on separation in AP, Applied general topology, 4.2 (2003), 475-486.
  • Lowen, R., and Verwulgen, S., Approach vector spaces, Houston J. Math , 30.4 (2004), 1127-1142.
  • Lowen, R., Index Analysis: Approach theory at work, Springer, 2015.
  • 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.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Mehmet Baran 0000-0001-9802-3718

Muhammad Qasım Bu kişi benim 0000-0001-9485-8072

Yayımlanma Tarihi 1 Şubat 2019
Gönderilme Tarihi 27 Şubat 2018
Kabul Tarihi 19 Nisan 2018
Yayımlandığı Sayı Yıl 2019 Cilt: 68 Sayı: 1

Kaynak Göster

APA Baran, M., & Qasım, M. (2019). T₁ Approach Spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 784-800. https://doi.org/10.31801/cfsuasmas.478632
AMA Baran M, Qasım M. T₁ Approach Spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2019;68(1):784-800. doi:10.31801/cfsuasmas.478632
Chicago Baran, Mehmet, ve Muhammad Qasım. “T₁ Approach Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 1 (Şubat 2019): 784-800. https://doi.org/10.31801/cfsuasmas.478632.
EndNote Baran M, Qasım M (01 Şubat 2019) T₁ Approach Spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 784–800.
IEEE M. Baran ve M. Qasım, “T₁ Approach Spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 1, ss. 784–800, 2019, doi: 10.31801/cfsuasmas.478632.
ISNAD Baran, Mehmet - Qasım, Muhammad. “T₁ Approach Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (Şubat 2019), 784-800. https://doi.org/10.31801/cfsuasmas.478632.
JAMA Baran M, Qasım M. T₁ Approach Spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:784–800.
MLA Baran, Mehmet ve Muhammad Qasım. “T₁ Approach Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 1, 2019, ss. 784-00, doi:10.31801/cfsuasmas.478632.
Vancouver Baran M, Qasım M. T₁ Approach Spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):784-800.

Cited By

On the categories of probabilistic approach groups: Actions
Filomat
https://doi.org/10.2298/FIL2316413A
The Fell approach structure
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
https://doi.org/10.31801/cfsuasmas.1224326
https://doi.org/

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

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.