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Local T_2 Constant Filter Convergence Spaces

Year 2018, Volume: 10, 88 - 94, 29.12.2018

Ayhan Erciyes , Tesnim Meryem Baran

Abstract

The aim of this paper is to characterize local Hausdorff constant filter convergence spaces and show that they are hereditary, productive and coproductive.

Keywords

Topological category local Hausdorff spaces constant filter convergence spaces products

References

  • Adamek, J., Herrlich, H., Strecker, G.E., Abstract and Concrete Categories, New York, USA: Wiley, 1990.
  • Baran, M., Separation Properties, Indian J. Pure Appl. Math., 23(1991), 333–341.
  • Baran, M., The notion of closedness in topological categories, Comment. Math. Univ. Carolinae, 34(1993), 383–395.
  • Baran, M., Separation Properties In Category Of Stack Convergence Spaces, Turkish Journal of Mathematics, 17(1993), 55–62.
  • Baran, M., Generalized Local Separation Properties, Indian J. pure appl. 25(1994), 615–620.
  • Baran, M., Separation Properties In Categories Of Constant Convergence Spaces, Turkish Journal of Mathematics, 18(1994), 238–248.
  • Baran M. and Altindis, H., T0-Objects in Topological Categories, J. Univ. Kuwait (Sci) Math. Hungar. 22(1995), 123–127.
  • Baran M. and Altindis, H., T2-Objects in Topological Categories, Acta Math. Hungar. 71(1996), 41–48.
  • 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), 59–69.
  • Baran, M., Completely regular objects and normal objects in topological categories, Acta Math. Hungar 1998; 80: 211-224.
  • Baran, M., Closure operators in convergence spaces, Acta Math. Hungar. 87(2000), 33–45.
  • Baran, M., Compactness, perfectness, separation, minimality and closedness with respect to closure operators, Applied Categorical Structures, 10(2002), 403–415.
  • Baran, M., PreT2 Objects In Topological Categories, Appl. Categor. Struct., 17(2009), 591–602.
  • Baran, M. and Al-Safar, J., Quotient-Reflective and Bireflective Subcategories of the category of Preordered Sets, Topology and its Appl., 158(2011), 2076–2084.
  • Baran, M. Kula, S., Baran, T. M., and Qasim, M., Closure operators in semiuniform convergence space, Filomat, 30 (2016), 131–140.
  • Bourbaki, N., Topologie generale. Chapitre 1 et 2. Actualites Sci. Ind., 1940.
  • Cartan, H., Filtres et ultrafiltres, CR Acad. Paris, 205(1937), 777–779.
  • Cartan, H., Th´eorie des filtres, CR Acad. Paris, 205(1937), 595–598.
  • Choquet, G.,Convergences, Ann. Univ. Grenoble Sect. Sci. Math. Phys. (NS) 23.(1948), 57–112.
  • Cook, H.C., and Fisher, H.R., On equicontinuity and continuous convergence, Math. Ann. 159(1965), 94–104.
  • Dikranjan, D. and Giuli, E., Closure operators I, Topology and its Appl., 27(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.
  • Erciyes, A., Baran, M., Local Pre-Hausdor_ Constant Filter Convergence Spaces, Turk. J. Math. Comput. Sci. 2018.
  • Fischer, H.R., Limesraume, Math. Ann. 137(1959), 269–303.
  • Herrlich, H., Topological functors, Gen Topology Appl 4(1974), 125–142.
  • Johnstone, P.T., Topos Theory, L.M.S Mathematics Monograph: No. 10. Academic, New York 1977.
  • Kent, D.C., Convergence functions and their related topologies, Fund. Math. 54(1964), 125–133.
  • Kowalsky, H.J., Beitrage zur topologischen algebra, Math. Nachrichten 11(1954), 143–185.
  • MacLane, S., Moerdijk, I., Sheaves in Geometry and Logic., Springer, New York, 1992.
  • Lowen-Colebunders, E., Function Classes of Cauchy Continuous Maps, New York USA; Marcel Dekker Inc, 1989.
  • Nel, L.D., Initially structured categories and cartesian closedness, Canadian J.Math., 27(1975), 1361–1377.
  • Preuss, G., Theory of Topological Structures, An Approach to Topological Categories, Dordrecht; D Reidel Publ Co, 1988.
  • Preuss, G., Foundations of topology, An approach to Convenient topology, Kluwer Academic Publishers, Dordrecht, 2002.
  • Robertson, W., Convergence as a nearness concept, Ph.D. thesis, University of Ottawa at Carleton, 1975.
  • Schwarz, F. Hannover, TU., Connections Between Convergence And Nearness, The series Lecture Notes in Mathematics, 719(1979), 345–357.

Year 2018, Volume: 10, 88 - 94, 29.12.2018

Ayhan Erciyes , Tesnim Meryem Baran

Abstract

References

  • Adamek, J., Herrlich, H., Strecker, G.E., Abstract and Concrete Categories, New York, USA: Wiley, 1990.
  • Baran, M., Separation Properties, Indian J. Pure Appl. Math., 23(1991), 333–341.
  • Baran, M., The notion of closedness in topological categories, Comment. Math. Univ. Carolinae, 34(1993), 383–395.
  • Baran, M., Separation Properties In Category Of Stack Convergence Spaces, Turkish Journal of Mathematics, 17(1993), 55–62.
  • Baran, M., Generalized Local Separation Properties, Indian J. pure appl. 25(1994), 615–620.
  • Baran, M., Separation Properties In Categories Of Constant Convergence Spaces, Turkish Journal of Mathematics, 18(1994), 238–248.
  • Baran M. and Altindis, H., T0-Objects in Topological Categories, J. Univ. Kuwait (Sci) Math. Hungar. 22(1995), 123–127.
  • Baran M. and Altindis, H., T2-Objects in Topological Categories, Acta Math. Hungar. 71(1996), 41–48.
  • 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), 59–69.
  • Baran, M., Completely regular objects and normal objects in topological categories, Acta Math. Hungar 1998; 80: 211-224.
  • Baran, M., Closure operators in convergence spaces, Acta Math. Hungar. 87(2000), 33–45.
  • Baran, M., Compactness, perfectness, separation, minimality and closedness with respect to closure operators, Applied Categorical Structures, 10(2002), 403–415.
  • Baran, M., PreT2 Objects In Topological Categories, Appl. Categor. Struct., 17(2009), 591–602.
  • Baran, M. and Al-Safar, J., Quotient-Reflective and Bireflective Subcategories of the category of Preordered Sets, Topology and its Appl., 158(2011), 2076–2084.
  • Baran, M. Kula, S., Baran, T. M., and Qasim, M., Closure operators in semiuniform convergence space, Filomat, 30 (2016), 131–140.
  • Bourbaki, N., Topologie generale. Chapitre 1 et 2. Actualites Sci. Ind., 1940.
  • Cartan, H., Filtres et ultrafiltres, CR Acad. Paris, 205(1937), 777–779.
  • Cartan, H., Th´eorie des filtres, CR Acad. Paris, 205(1937), 595–598.
  • Choquet, G.,Convergences, Ann. Univ. Grenoble Sect. Sci. Math. Phys. (NS) 23.(1948), 57–112.
  • Cook, H.C., and Fisher, H.R., On equicontinuity and continuous convergence, Math. Ann. 159(1965), 94–104.
  • Dikranjan, D. and Giuli, E., Closure operators I, Topology and its Appl., 27(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.
  • Erciyes, A., Baran, M., Local Pre-Hausdor_ Constant Filter Convergence Spaces, Turk. J. Math. Comput. Sci. 2018.
  • Fischer, H.R., Limesraume, Math. Ann. 137(1959), 269–303.
  • Herrlich, H., Topological functors, Gen Topology Appl 4(1974), 125–142.
  • Johnstone, P.T., Topos Theory, L.M.S Mathematics Monograph: No. 10. Academic, New York 1977.
  • Kent, D.C., Convergence functions and their related topologies, Fund. Math. 54(1964), 125–133.
  • Kowalsky, H.J., Beitrage zur topologischen algebra, Math. Nachrichten 11(1954), 143–185.
  • MacLane, S., Moerdijk, I., Sheaves in Geometry and Logic., Springer, New York, 1992.
  • Lowen-Colebunders, E., Function Classes of Cauchy Continuous Maps, New York USA; Marcel Dekker Inc, 1989.
  • Nel, L.D., Initially structured categories and cartesian closedness, Canadian J.Math., 27(1975), 1361–1377.
  • Preuss, G., Theory of Topological Structures, An Approach to Topological Categories, Dordrecht; D Reidel Publ Co, 1988.
  • Preuss, G., Foundations of topology, An approach to Convenient topology, Kluwer Academic Publishers, Dordrecht, 2002.
  • Robertson, W., Convergence as a nearness concept, Ph.D. thesis, University of Ottawa at Carleton, 1975.
  • Schwarz, F. Hannover, TU., Connections Between Convergence And Nearness, The series Lecture Notes in Mathematics, 719(1979), 345–357.
There are 36 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Ayhan Erciyes 0000-0002-0942-5182

Tesnim Meryem Baran This is me

Publication Date December 29, 2018
Published in Issue Year 2018 Volume: 10

Cite

APA Erciyes, A., & Baran, T. M. (2018). Local T_2 Constant Filter Convergence Spaces. Turkish Journal of Mathematics and Computer Science, 10, 88-94.
AMA Erciyes A, Baran TM. Local T_2 Constant Filter Convergence Spaces. TJMCS. December 2018;10:88-94.
Chicago Erciyes, Ayhan, and Tesnim Meryem Baran. “Local T_2 Constant Filter Convergence Spaces”. Turkish Journal of Mathematics and Computer Science 10, December (December 2018): 88-94.
EndNote Erciyes A, Baran TM (December 1, 2018) Local T_2 Constant Filter Convergence Spaces. Turkish Journal of Mathematics and Computer Science 10 88–94.
IEEE A. Erciyes and T. M. Baran, “Local T_2 Constant Filter Convergence Spaces”, TJMCS, vol. 10, pp. 88–94, 2018.
ISNAD Erciyes, Ayhan - Baran, Tesnim Meryem. “Local T_2 Constant Filter Convergence Spaces”. Turkish Journal of Mathematics and Computer Science 10 (December 2018), 88-94.
JAMA Erciyes A, Baran TM. Local T_2 Constant Filter Convergence Spaces. TJMCS. 2018;10:88–94.
MLA Erciyes, Ayhan and Tesnim Meryem Baran. “Local T_2 Constant Filter Convergence Spaces”. Turkish Journal of Mathematics and Computer Science, vol. 10, 2018, pp. 88-94.
Vancouver Erciyes A, Baran TM. Local T_2 Constant Filter Convergence Spaces. TJMCS. 2018;10:88-94.
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