Research Article
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Year 2020, Volume: 33 Issue: 2, 446 - 454, 01.06.2020
https://doi.org/10.35378/gujs.602155

Abstract

References

  • Cartan, H., “Theorie des filters”, C.R. Acad. Sc. Paris, 205: 595-598, (1937).
  • Cartan, H., “Filtres et ultrafiltres”, C.R. Acad. Sc. Paris, 205: 777–779, (1937).
  • Schwarz, F.,“Connections Between Convergence And Nearness”, The series Lecture Notes in Mathematics, 719: 345–354, (1978).
  • Baran, M., “Separation properties”, Indian J. Pure Appl. Math. 23: 333-341, (1991).
  • Baran, M., “The Notion of Closedness in Topological Categories”, Comment. Math. Univ. Carolinae 34: 383-395, (1993).
  • Adamek, J., Herrlich, H., Strecker, G.E., “Abstract and Concrete Categories”, Wiley, New York, (1990).
  • Nel, L.D., “Initially Structured Categories and Cartesian Closedness”, Canadian J.Math., 27: 1361-1377, (1975).
  • Baran, M., “Separation Properties In topological Categories” Mathematica Balkanica, 10: 39-48, (1996).
  • Baran, M., “Stacks and filters”, Turkish J. of Math.Doğa, 16: 95-108, (1992).
  • Baran, M., “T_3 and T_4-objects in topological categories”, Indian J. Pure Appl. Math. 29: 59-69, (1998).
  • Erciyes, A., Baran, M., “Local Pre-Hausdorff Constant Filter Convergence Spaces” Turk. J. Math. Comput. Sci., 10: 82-87, (2018).
  • Baran, T.M., “Local T_2 Extended Pseudo-Quasi-Semi Metric Spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat, 68(2): 2117-2127, (2019).
  • Kula, M., Separation properties at p for the topological category of Cauchy Spaces. Acta Math. Hungar. 136: 1-15, (2012).
  • Lowen-Colebunders, E., “Function Classes of Cauchy Continuous Maps”, New York USA; Marcel Dekker Inc, (1989).
  • Baran, T.M., Kula, M., “Local Pre Hausdorff Extended Pseudo-Quasi-Semi Metric Spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat, 68(1): 862-870, (2019).
  • Baran, M., “PreT_2 Objects In Topological Categories”, Appl. Categor. Struct., 17: 591-602, (2009).

Local T_3 Constant Filter Convergence Spaces

Year 2020, Volume: 33 Issue: 2, 446 - 454, 01.06.2020
https://doi.org/10.35378/gujs.602155

Abstract

In this paper, we characterize each of local T_3(resp. T_3', ST _3, ST_3') constant filter convergence spaces and investigate the relationships among these various forms. We show that the full subcategories T_3 ConFCO and ST_3 ConFCO (resp. T_3'ConFCO and ST_3'ConFCO) of ConFCO are isomorphic categories. Moreover, we show that if a constant filter convergence space (B,K) is T _3 (resp. T_3^' , ST _3 or ST_3') at p and M⊂B with p∈M, then M is T _3 (resp. T_3^' ) at p.

References

  • Cartan, H., “Theorie des filters”, C.R. Acad. Sc. Paris, 205: 595-598, (1937).
  • Cartan, H., “Filtres et ultrafiltres”, C.R. Acad. Sc. Paris, 205: 777–779, (1937).
  • Schwarz, F.,“Connections Between Convergence And Nearness”, The series Lecture Notes in Mathematics, 719: 345–354, (1978).
  • Baran, M., “Separation properties”, Indian J. Pure Appl. Math. 23: 333-341, (1991).
  • Baran, M., “The Notion of Closedness in Topological Categories”, Comment. Math. Univ. Carolinae 34: 383-395, (1993).
  • Adamek, J., Herrlich, H., Strecker, G.E., “Abstract and Concrete Categories”, Wiley, New York, (1990).
  • Nel, L.D., “Initially Structured Categories and Cartesian Closedness”, Canadian J.Math., 27: 1361-1377, (1975).
  • Baran, M., “Separation Properties In topological Categories” Mathematica Balkanica, 10: 39-48, (1996).
  • Baran, M., “Stacks and filters”, Turkish J. of Math.Doğa, 16: 95-108, (1992).
  • Baran, M., “T_3 and T_4-objects in topological categories”, Indian J. Pure Appl. Math. 29: 59-69, (1998).
  • Erciyes, A., Baran, M., “Local Pre-Hausdorff Constant Filter Convergence Spaces” Turk. J. Math. Comput. Sci., 10: 82-87, (2018).
  • Baran, T.M., “Local T_2 Extended Pseudo-Quasi-Semi Metric Spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat, 68(2): 2117-2127, (2019).
  • Kula, M., Separation properties at p for the topological category of Cauchy Spaces. Acta Math. Hungar. 136: 1-15, (2012).
  • Lowen-Colebunders, E., “Function Classes of Cauchy Continuous Maps”, New York USA; Marcel Dekker Inc, (1989).
  • Baran, T.M., Kula, M., “Local Pre Hausdorff Extended Pseudo-Quasi-Semi Metric Spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat, 68(1): 862-870, (2019).
  • Baran, M., “PreT_2 Objects In Topological Categories”, Appl. Categor. Struct., 17: 591-602, (2009).
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Ayhan Erciyes 0000-0002-0942-5182

Tesnim Meryem Baran This is me 0000-0001-6639-8654

Publication Date June 1, 2020
Published in Issue Year 2020 Volume: 33 Issue: 2

Cite

APA Erciyes, A., & Baran, T. M. (2020). Local T_3 Constant Filter Convergence Spaces. Gazi University Journal of Science, 33(2), 446-454. https://doi.org/10.35378/gujs.602155
AMA Erciyes A, Baran TM. Local T_3 Constant Filter Convergence Spaces. Gazi University Journal of Science. June 2020;33(2):446-454. doi:10.35378/gujs.602155
Chicago Erciyes, Ayhan, and Tesnim Meryem Baran. “Local T_3 Constant Filter Convergence Spaces”. Gazi University Journal of Science 33, no. 2 (June 2020): 446-54. https://doi.org/10.35378/gujs.602155.
EndNote Erciyes A, Baran TM (June 1, 2020) Local T_3 Constant Filter Convergence Spaces. Gazi University Journal of Science 33 2 446–454.
IEEE A. Erciyes and T. M. Baran, “Local T_3 Constant Filter Convergence Spaces”, Gazi University Journal of Science, vol. 33, no. 2, pp. 446–454, 2020, doi: 10.35378/gujs.602155.
ISNAD Erciyes, Ayhan - Baran, Tesnim Meryem. “Local T_3 Constant Filter Convergence Spaces”. Gazi University Journal of Science 33/2 (June 2020), 446-454. https://doi.org/10.35378/gujs.602155.
JAMA Erciyes A, Baran TM. Local T_3 Constant Filter Convergence Spaces. Gazi University Journal of Science. 2020;33:446–454.
MLA Erciyes, Ayhan and Tesnim Meryem Baran. “Local T_3 Constant Filter Convergence Spaces”. Gazi University Journal of Science, vol. 33, no. 2, 2020, pp. 446-54, doi:10.35378/gujs.602155.
Vancouver Erciyes A, Baran TM. Local T_3 Constant Filter Convergence Spaces. Gazi University Journal of Science. 2020;33(2):446-54.