Finally, we investigate the relationships between ∂-connected object and (strongly) connected object in the topological category of proximity space.Mathematics Subject Classification (2010). 54B30, 54D10, 54A05, 54E05, 18B99, 18D15
📌 3 Key Takeaways
🎯
Objective & Hypothesis:Inthispaper,anexplicitcharacterizationoftheseparationproperties ST2,∆T2, ST3,∆T3 and Tychonoff objects are given in the topological category of proximity space.
📊
Key Findings & Data:Moreover, we investigate the relationships among ST2, ∆T2, ST3, ∆T3, the separation properties at a point p, the generalized separation properties Ti, i = 0,1,2, T0, T1, T2 and Tychonoff objects in this category.
💡
Conclusion & Impact:Finally, we investigate the relationships between ∂-connected object and (strongly) connected object in the topological category of proximity space.Mathematics Subject Classification (2010). 54B30, 54D10, 54A05, 54E05, 18B99, 18D15
🔬Design:Research Article
📍Scope:2010 Verileri
⚙️Variables:Domain Parameters
Abstract
Inthispaper,anexplicitcharacterizationoftheseparationproperties ST2,∆T2, ST3,∆T3 and Tychonoff objects are given in the topological category of proximity space. Furthermore, the (strongly) compact object and ∂-connected object are also characterized in the category of proximity space. Moreover, we investigate the relationships among ST2, ∆T2, ST3, ∆T3, the separation properties at a point p, the generalized separation properties Ti, i = 0,1,2, T0, T1, T2 and Tychonoff objects in this category. Finally, we investigate the relationships between ∂-connected object and (strongly) connected object in the topological category of proximity space.Mathematics Subject Classification (2010). 54B30, 54D10, 54A05, 54E05, 18B99, 18D15
🔖
Cite This Article
Kula, M. (2022). ST2, ∆T2, ST3, ∆T3, Tychonoff, compact and ∂-connected objects in the category of proximity spaces. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 2, 490–500. https://ajindex.com/articles/529790
J. Adámek, H. Herrlich and G.E. Strecker, Abstract and Concrete Categories, John Wiley and Sons, New York, 1990
M. Baran, Separation properties, Indian J. Pure Appl. Math. 23 (5), 333-341, 1992
M. Baran, Separation Properties at p for the topological categories of reflexive relation spaces and preordered spaces, Math. Balkanica (N.S.) 6 (2), 193-198, 1992
M. Baran, The notion of closedness in topological categories, Comment. Math. Univ. Carolin. 34 (2), 383-395, 1993
M. Baran, Generalized local separation properties, Indian J. Pure Appl. Math. 25 (6), 615-620, 1994
M. Baran, Separation properties in topological categories, Math. Balkanica (N.S.) 10 (1), 39-48, 1996
M. Baran, A notion of compactness in topological categories, Publ. Math. Debrecen 50 (3-4), 221-234, 1997
M. Baran, T3 and T4-objects in topological categories, Indian J. Pure Appl. Math. 29 (1), 59-69, 1998
M. Baran, Completely regular objects and normal objects in topological categories, Acta Math. Hungar. 80 (3), 211-224, 1998
M. Baran, Closure operators in convergence spaces, Acta Math. Hungar. 87 (1-2), 33-45, 2000
M. Baran, Compactness, perfectness, separation, minimality and closedness with re- spect to closure operators, Appl. Categ. Structures 10 (4), 403-415, 2002
M. Baran, PreT2-objects in topological categories, Appl. Categ. Structures 17 (6), 591-602, 2009, DOI: 10.1007/s10485-008-9161-4
M. Baran and J. Al-Safar, Quotient-reflective and bireflective subcategories of the category of preordered sets, Topology Appl. 158 (15), 2076-2084, 2011, DOI 10.1016/j.topol.2011.06.043
M. Baran and M. Kula, A note on separation and compactness in categories of con- vergence spaces, Proceedings of the International Conference on Applicable General Topology, Ankara, 2001, Appl. Gen. Topol. 4 (1), 1-13, 2003
M. Baran and M. Kula, A note on connectedness, Publ. Math. Debrecen 68 (3-4), 489-501, 2006
N. Bourbaki, General Topology, Addison-Wesley Publ. Co., 1966
D. Dikranjan and E. Giuli, Closure operators I, Proceedings of the 8th international conference on categorical topology, L’Aquila, 1986, Topology Appl. 27 (2), 129-143, 1987
V.A. Efremovich, Infinitesimal spaces (Russian), Doklady Akad. Nauk SSSR (N.S.) 76, 341-343, 1951
L.M. Friedler, Mappings of Proximity Spaces, PH.D. Thesis, University of Alberta, 1972
L.M. Friedler, Quotients of proximity spaces, Proc. Amer. Math. Soc. 37 (2), 589-5