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Year 2020, Volume: 8 Issue: 1, 185 - 191, 15.04.2020

Ayhan Erciyes Tesnim Meryem Baran Muhammad Qasim

Abstract

References

  • [1] J. Adamek, Herrlich, H., Strecker, G.E., Abstract and Concrete Categories, New York, USA, Wiley, 1990.
  • [2] M. Baran, Separation Properties, Indian J. Pure Appl. Math., 23 (1992), 333-341.
  • [3] M. Baran, The Notion of Closedness in Topological Categories, Comment. Math. Univ. Carolinae, 34 (1993), 383-395.
  • [4] M. Baran, Separation Properties in Categories of Constant Convergence Spaces, Turkish Journal of Mathematics, 18 (1994), 238-248.
  • [5] M.Baran, A Notion of Compactness in Topological Categories, Publ. Math. Debrecen, 50 (1997), 221-234.
  • [6] M. Baran, Closure Operators in Convergence Spaces, Acta Math. Hungar., 87 (2000), 33-45.
  • [7] M. Baran, Compactness, Perfectness, Separation, Minimality and Closedness with Respect to Closure Operators, Applied Categorical Structures, 10 (2002), 403-415.
  • [8] M. Baran and J. Al-Safar, Quotient-Reflective and Bireflective Subcategories of the Category of Preordered Sets, Topology and its Appl., 158 (2011), 2076-2084.
  • [9] M. Baran, Stacks and Filters, Do˘ga Mat., 16 (1992), 95-108.
  • [10] M. Baran, S. Kula, T.M. Baran and M. Qasim, Closure Operators in Semiuniform Convergence Spaces, Filomat 30 (2016), 131-140.
  • [11] M. Clementino, E. Giuli, and W. Tholen, Topology in a Category :Compactness, Port. Math., 53 (1996), 397-433.
  • [12] D. Dikranjan and E. Giuli, Closure Operators I, Topology Appl., 27 (1987), 129-143.
  • [13] D. Dikranjan and W. Tholen, Categorical Structure of Closure Operators, Kluwer Academic Publishers, Dordrecht, 1995.
  • [14] H. Herrlich, G. Salicrup and G.E. Strecker, Factorizations, Denseness, Separation, and Relatively Compact Objects, Topology Appl., 27 (1987), 157-169.
  • [15] M. Kula and M. Baran, A Note on Connectedness, Publ. Math. Debrecen, 68 (2006), 489-501.
  • [16] W. Robertson, Convergence as a Nearness Concept, Ph.D. Thesis, University of Ottawa at Carleton, 1975.
  • [17] F. Schwarz and TU. Hannover, Connections Between Convergence And Nearness, The series Lecture Notes in Mathematics, 719 (1979), 345-357.

Closure Operators in Constant Filter Convergence Spaces

Year 2020, Volume: 8 Issue: 1, 185 - 191, 15.04.2020

Ayhan Erciyes Tesnim Meryem Baran Muhammad Qasim

Abstract

In this paper, we define two notions of closure in the category of constant filter convergence spaces which satisfy productivity, idempotency, and hereditariness. Moreover, by using these closure operators, we characterize each of $T_{i}$ constant filter convergence spaces, $i=0,1,2$ and show that each of these subcategories consisting of $T_{i}$ constant filter convergence spaces, $i=0,1,2$, are epireflective. Finally, we investigate the relationship among these subcategories.

Keywords

Topological category closure operator constant filter convergence spaces

References

  • [1] J. Adamek, Herrlich, H., Strecker, G.E., Abstract and Concrete Categories, New York, USA, Wiley, 1990.
  • [2] M. Baran, Separation Properties, Indian J. Pure Appl. Math., 23 (1992), 333-341.
  • [3] M. Baran, The Notion of Closedness in Topological Categories, Comment. Math. Univ. Carolinae, 34 (1993), 383-395.
  • [4] M. Baran, Separation Properties in Categories of Constant Convergence Spaces, Turkish Journal of Mathematics, 18 (1994), 238-248.
  • [5] M.Baran, A Notion of Compactness in Topological Categories, Publ. Math. Debrecen, 50 (1997), 221-234.
  • [6] M. Baran, Closure Operators in Convergence Spaces, Acta Math. Hungar., 87 (2000), 33-45.
  • [7] M. Baran, Compactness, Perfectness, Separation, Minimality and Closedness with Respect to Closure Operators, Applied Categorical Structures, 10 (2002), 403-415.
  • [8] M. Baran and J. Al-Safar, Quotient-Reflective and Bireflective Subcategories of the Category of Preordered Sets, Topology and its Appl., 158 (2011), 2076-2084.
  • [9] M. Baran, Stacks and Filters, Do˘ga Mat., 16 (1992), 95-108.
  • [10] M. Baran, S. Kula, T.M. Baran and M. Qasim, Closure Operators in Semiuniform Convergence Spaces, Filomat 30 (2016), 131-140.
  • [11] M. Clementino, E. Giuli, and W. Tholen, Topology in a Category :Compactness, Port. Math., 53 (1996), 397-433.
  • [12] D. Dikranjan and E. Giuli, Closure Operators I, Topology Appl., 27 (1987), 129-143.
  • [13] D. Dikranjan and W. Tholen, Categorical Structure of Closure Operators, Kluwer Academic Publishers, Dordrecht, 1995.
  • [14] H. Herrlich, G. Salicrup and G.E. Strecker, Factorizations, Denseness, Separation, and Relatively Compact Objects, Topology Appl., 27 (1987), 157-169.
  • [15] M. Kula and M. Baran, A Note on Connectedness, Publ. Math. Debrecen, 68 (2006), 489-501.
  • [16] W. Robertson, Convergence as a Nearness Concept, Ph.D. Thesis, University of Ottawa at Carleton, 1975.
  • [17] F. Schwarz and TU. Hannover, Connections Between Convergence And Nearness, The series Lecture Notes in Mathematics, 719 (1979), 345-357.
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Ayhan Erciyes

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

Muhammad Qasim 0000-0003-0279-5305

Publication Date April 15, 2020
Submission Date January 28, 2020
Acceptance Date April 5, 2020
Published in Issue Year 2020 Volume: 8 Issue: 1

Cite

APA Erciyes, A., Baran, T. M., & Qasim, M. (2020). Closure Operators in Constant Filter Convergence Spaces. Konuralp Journal of Mathematics, 8(1), 185-191.
AMA Erciyes A, Baran TM, Qasim M. Closure Operators in Constant Filter Convergence Spaces. Konuralp J. Math. April 2020;8(1):185-191.
Chicago Erciyes, Ayhan, Tesnim Meryem Baran, and Muhammad Qasim. “Closure Operators in Constant Filter Convergence Spaces”. Konuralp Journal of Mathematics 8, no. 1 (April 2020): 185-91.
EndNote Erciyes A, Baran TM, Qasim M (April 1, 2020) Closure Operators in Constant Filter Convergence Spaces. Konuralp Journal of Mathematics 8 1 185–191.
IEEE A. Erciyes, T. M. Baran, and M. Qasim, “Closure Operators in Constant Filter Convergence Spaces”, Konuralp J. Math., vol. 8, no. 1, pp. 185–191, 2020.
ISNAD Erciyes, Ayhan et al. “Closure Operators in Constant Filter Convergence Spaces”. Konuralp Journal of Mathematics 8/1 (April 2020), 185-191.
JAMA Erciyes A, Baran TM, Qasim M. Closure Operators in Constant Filter Convergence Spaces. Konuralp J. Math. 2020;8:185–191.
MLA Erciyes, Ayhan et al. “Closure Operators in Constant Filter Convergence Spaces”. Konuralp Journal of Mathematics, vol. 8, no. 1, 2020, pp. 185-91.
Vancouver Erciyes A, Baran TM, Qasim M. Closure Operators in Constant Filter Convergence Spaces. Konuralp J. Math. 2020;8(1):185-91.
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