Yıl: 2022 Cilt: 46 Sayı: 1 Sayfa Aralığı: 299 - 310 Metin Dili: İngilizce DOI: 10.3906/mat-2109-95 İndeks Tarihi: 19-07-2022

Sober spaces

Öz:
The goal of this paper is to introduce various forms of sober objects in a topological category and investigate the relationships among these various forms. Moreover, we characterize quasi-sober objects, $T_{0}$ objects and each of various forms of sober objects in some topological categories and give some invariance properties of them. Finally, we compare our results with some well-known results in the category of topological spaces.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Baran M. Separation properties. Indian Journal Pure Applied Mathematics 1991; 23 (5): 333-341.
  • [2] Baran M. The notion of closedness in topological categories. Commentationes Mathematicae Universitatis Carolinae 1993; 34 (2): 383-395.
  • [3] Baran M, Altindis H. $T_0$ -objects in topological categories, Kuwait Journal of Science 1995; (22): 123-127.
  • [4] Baran M. T2 -objects in categories of filter and local filter convergence spaces. Turkish Journal of Mathematics 1996; 159-168.
  • [5] Baran M. Compactness, perfectness, separation, minimality and closedness with respect to closure operators. Applied Categorical Structures 2002; (10): 403-415.
  • [6] Baran M, Kula S, Baran TM, Qasim M. Closure operators in semi uniform convergence spaces. Filomat 2016; (30): 131-140.
  • [7] Baran TM. Closedness, separation and connectedness in pseudo-quasi-semi metric spaces. Filomat 2020; (34): 14, 4757-4766. doi: 10.2298/FIL2014757B
  • [8] Giuli E, Dikranjan D. Closure operators I. Topology and its Applications 1987; (27): 129-143.
  • [9] Tholen W, Dikranjan D. Categorical structure of closure operators. Kluwer Academic Publishers, Dordrecht, 1995.
  • [10] Erciyes A, Baran TM, Qasim M. Closure operators constant filter convergence spaces. Konuralp Journal of Mathematics 2020; 185-191.
  • [11] Erciyes A, Baran TM. $T_4$ , Urysohn lemma, and Tietze extension theorem for constant filter convergence spaces. Turkish Journal of Mathematics 2021; 843-855.
  • [12] Dieudonné JA, Grothendieck A. Eléments de géométrie algébrique, Springer, New York, 1971 (in French).
  • [13] Hong SS. Extensive subcategory of the category of $T_0$ -spaces. Canadian Journal Mathematics 1975; (27): 318-331.
  • [14] Kula M, Baran TM. Separation axioms, Urysohn’s lemma and Tietze extension theorem for extended pseudo-quasisemi metric spaces. Filomat 2022. to appear.
  • [15] Larrecq JG. Non-Hausdorff Topology and Domain Theory, Cambridge University Press, 2013.
  • [16] Mielke MV. Convenient categories for internal singular algebraic topology. Illinois Journal of Mathematics 1983.
  • [17] Marny Th. Rechts-Bikategoriestrukturen in topologischen Kategorien, Dissertation, Freie Universität Berlin, 1973 (in German).
  • [18] Preuss G. Theory of Topological Structures, An Approach to topological Categories, D. Reidel Publ. Co., Dordrecht, 1988.
  • [19] Qasim M, Baran M, Abughalwa H. Closure operator in convergence approach spaces. Turkish Journal of Mathematics 2021; 139-152.
  • [20] Weck-Schwarz S. T0 -objects and separated objects in topological categories. Quaestiones Mathematicae 1991; (14): 315-325.
APA Baran M, Abughalwa H (2022). Sober spaces. , 299 - 310. 10.3906/mat-2109-95
Chicago Baran Mehmet,Abughalwa Hassan Sober spaces. (2022): 299 - 310. 10.3906/mat-2109-95
MLA Baran Mehmet,Abughalwa Hassan Sober spaces. , 2022, ss.299 - 310. 10.3906/mat-2109-95
AMA Baran M,Abughalwa H Sober spaces. . 2022; 299 - 310. 10.3906/mat-2109-95
Vancouver Baran M,Abughalwa H Sober spaces. . 2022; 299 - 310. 10.3906/mat-2109-95
IEEE Baran M,Abughalwa H "Sober spaces." , ss.299 - 310, 2022. 10.3906/mat-2109-95
ISNAD Baran, Mehmet - Abughalwa, Hassan. "Sober spaces". (2022), 299-310. https://doi.org/10.3906/mat-2109-95
APA Baran M, Abughalwa H (2022). Sober spaces. Turkish Journal of Mathematics, 46(1), 299 - 310. 10.3906/mat-2109-95
Chicago Baran Mehmet,Abughalwa Hassan Sober spaces. Turkish Journal of Mathematics 46, no.1 (2022): 299 - 310. 10.3906/mat-2109-95
MLA Baran Mehmet,Abughalwa Hassan Sober spaces. Turkish Journal of Mathematics, vol.46, no.1, 2022, ss.299 - 310. 10.3906/mat-2109-95
AMA Baran M,Abughalwa H Sober spaces. Turkish Journal of Mathematics. 2022; 46(1): 299 - 310. 10.3906/mat-2109-95
Vancouver Baran M,Abughalwa H Sober spaces. Turkish Journal of Mathematics. 2022; 46(1): 299 - 310. 10.3906/mat-2109-95
IEEE Baran M,Abughalwa H "Sober spaces." Turkish Journal of Mathematics, 46, ss.299 - 310, 2022. 10.3906/mat-2109-95
ISNAD Baran, Mehmet - Abughalwa, Hassan. "Sober spaces". Turkish Journal of Mathematics 46/1 (2022), 299-310. https://doi.org/10.3906/mat-2109-95