Closure operators in convergence approach spaces

Baran, Mehmet; Abughalwa, Hassan; Qasim, Muhammad

doi:10.3906/mat-2008-65

Closure operators in convergence approach spaces

Muhammad QASIM, (National University of Sciences and Technology (NUST), School of Natural Sciences (SNS), Department of Mathematics, Islamabad, Pakistan)

Mehmet BARAN, (Erciyes Üniversitesi, Fen Fakültesi, Matematik Bölümü, Kayseri, Türkiye)

Hassan ABUGHALWA (Erciyes Üniversitesi, Fen Fakültesi, Matematik Bölümü, Kayseri, Türkiye)

Turkish Journal of Mathematics

4 0

Yıl: 2021 Cilt: 45 Sayı: 1 Sayfa Aralığı: 139 - 152 Metin Dili: İngilizce DOI: 10.3906/mat-2008-65 İndeks Tarihi: 06-07-2022

Closure operators in convergence approach spaces

Öz:

In this paper, we characterize closed and strongly closed subsets of convergence approach spaces and introduce two notions of closure in the category of convergence approach spaces which satisfy idempotent, productive and (weakly) hereditary properties. Furthermore, we explicitly characterize each of Ti convergence approach spaces, i = 0, 1, 2 with respect to these closure operators and show that each of these subcategories of Ti convergence approach spaces, i = 0, 1, 2 are epireflective as well as we investigate the relationship among these subcategories. Finally, we characterize connected convergence approach spaces.

Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Adamek J, Herrlich H, Strecker GE. Abstract and Concrete Categories: The Joy of Cats (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts). New York, NY, USA: John Wiley & Sons, 1990.
[2] Baran M. Separation properties. Indian Journal of Pure & Applied Mathematics 1991; 23 (5): 333-341.
[3] Baran M. Stacks and filters. Doğa-Turkish Journal of Mathematics 1992; 16: 95-108.
[4] Baran M. The notion of closedness in topological categories. Commentationes Mathematicae Universitatis Carolinae 1993; 34 (2): 383-395.
[5] Baran M. A notion of compactness in topological categories. Publicationes Mathematicae Debrecen 1997; 50 (3-4): 221-234.
[6] Baran M. Closure operators in convergence spaces. Acta Mathematica Hungarica 2000; 87 (1-2): 33-45. doi: 10.1023/a:1006768916033
[7] Baran M. Compactness, perfectness, separation, minimality and closedness with respect to closure operators. Applied Categorical Structures 2002; 10: 403-415. doi: 10.1023/A:1016388102703
[8] Baran M, Kula M. A note on connectedness. Publicationes Mathematicae Debrecen 2006; 68 (3-4): 489-501.
[9] Baran M, Al-safar J. Quotient-reflective and bireflective subcategories of the category of preordered sets. Topology and its Applications 2011; 158 (15): 2076-2084. doi: 10.1016/j.topol.2011.06.043
[10] Baran M, Kula S, Baran TM, Qasim M. Closure operators in semiuniform convergence spaces. Filomat 2016; 30 (1): 131-140. doi: 10.2298/FIL1601131B
[11] Baran M, Qasim M. T1 approach spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 2019; 68 (1): 784-800. doi: 10.31801/cfsuasmas.478632
[12] Dikranjan D, Giuli E. Closure operators I. Topology and its Applications 1987; 27: 129-143.
[13] Dikranjan D, Tholen W. Categorical Structure of Closure Operators. Dordrecht, Netherlands: Kluwer Academic Publishers, 1995.
[14] Erciyes A, Baran TM, Qasim M. Closure operators in constant filter convergence spaces. Konuralp Journal of Mathematics 2020; 8 (1): 185-191.
[15] Berckmoes B, Lowen R, Van Casteren J. Approach theory meets probability theory. Topology and its Applications 2011; 158 (7): 836-852. doi: 10.1016/j.topol.2011.01.004
[16] Colebunders E, De Wachter S, Lowen R. Intrinsic approach spaces on domains. Topology and its Applications 2011; 158 (17): 2343-2355. doi: 10.1016/j.topol.2011.01.025
[17] Lowen E, Lowen R. Topological quasitopos hulls of categories containing topological and metric objects. Cahiers de topologie et géométrie différentielle catégoriques 1989; 30 (3): 213-228.
[18] Lowen R. Approach spaces a common supercategory of TOP and MET. Mathematische Nachrichten 1989; 141 (1): 183-226.
[19] Lowen R. Approach Spaces: The Missing Link in the Topology-Uniformity-Metric triad. Oxford, UK: Oxford University Press, 1997.
[20] Lowen R, Windels B. Approach groups. The Rocky Mountain Journal of Mathematics 2000; 30: 1057-1073.
[21] Lowen R, Verwulgen S. Approach vector spaces. Houston Journal of Mathematics 2004; 30 (4): 1127-1142.
[22] Lowen R. Index Analysis - Approach Theory at Work. London, UK: Springer-Verlag, 2015.
[23] Preuss G. Theory of Topological Structures - An Approach to Categorical Topology. Dordrecht, Netherlands: D. Reidel Publishing Company, 1988.
[24] Preuss G. Foundations of Topology - An Approach to Convenient Topology. Dordrecht, Netherlands: Kluwer Academic Publishers, 2002.
[25] Qasim M, Baran M. T0 Convergence approach spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 2020; 69 (1): 603-612. doi: 10.31801/cfsuasmas.609919

APA	Qasim M, Baran M, Abughalwa H (2021). Closure operators in convergence approach spaces . , 139 - 152. 10.3906/mat-2008-65
Chicago	Qasim Muhammad,Baran Mehmet,Abughalwa Hassan Closure operators in convergence approach spaces . (2021): 139 - 152. 10.3906/mat-2008-65
MLA	Qasim Muhammad,Baran Mehmet,Abughalwa Hassan Closure operators in convergence approach spaces . , 2021, ss.139 - 152. 10.3906/mat-2008-65
AMA	Qasim M,Baran M,Abughalwa H Closure operators in convergence approach spaces . . 2021; 139 - 152. 10.3906/mat-2008-65
Vancouver	Qasim M,Baran M,Abughalwa H Closure operators in convergence approach spaces . . 2021; 139 - 152. 10.3906/mat-2008-65
IEEE	Qasim M,Baran M,Abughalwa H "Closure operators in convergence approach spaces ." , ss.139 - 152, 2021. 10.3906/mat-2008-65
ISNAD	Qasim, Muhammad vd. "Closure operators in convergence approach spaces ". (2021), 139-152. https://doi.org/10.3906/mat-2008-65

APA	Qasim M, Baran M, Abughalwa H (2021). Closure operators in convergence approach spaces . Turkish Journal of Mathematics, 45(1), 139 - 152. 10.3906/mat-2008-65
Chicago	Qasim Muhammad,Baran Mehmet,Abughalwa Hassan Closure operators in convergence approach spaces . Turkish Journal of Mathematics 45, no.1 (2021): 139 - 152. 10.3906/mat-2008-65
MLA	Qasim Muhammad,Baran Mehmet,Abughalwa Hassan Closure operators in convergence approach spaces . Turkish Journal of Mathematics, vol.45, no.1, 2021, ss.139 - 152. 10.3906/mat-2008-65
AMA	Qasim M,Baran M,Abughalwa H Closure operators in convergence approach spaces . Turkish Journal of Mathematics. 2021; 45(1): 139 - 152. 10.3906/mat-2008-65
Vancouver	Qasim M,Baran M,Abughalwa H Closure operators in convergence approach spaces . Turkish Journal of Mathematics. 2021; 45(1): 139 - 152. 10.3906/mat-2008-65
IEEE	Qasim M,Baran M,Abughalwa H "Closure operators in convergence approach spaces ." Turkish Journal of Mathematics, 45, ss.139 - 152, 2021. 10.3906/mat-2008-65
ISNAD	Qasim, Muhammad vd. "Closure operators in convergence approach spaces ". Turkish Journal of Mathematics 45/1 (2021), 139-152. https://doi.org/10.3906/mat-2008-65