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ON Q-BITOPOLOGICAL SPACES | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 5، دوره 15، شماره 3، مرداد و شهریور 2018، صفحه 65-77 اصل مقاله (410.86 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2018.3950 | ||
| نویسندگان | ||
| Rana Noor1؛ Arun K. Srivastava2؛ Sheo Kumar Singh* 3 | ||
| 1Department of Mathematics, University of Allahabad, Allahabad-211 002, India | ||
| 2DST-Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi-221 005, India | ||
| 3Department of Mathematics, Mahatma Gandhi Central University Bihar, East Champaran-845 401, India | ||
| چکیده | ||
| We study here $T_{0}$-$Q$-bitopological spaces and sober $Q$-bitopological spaces and their relationship with two particular Sierpinski objects in the category of $Q$-bitopological spaces. The epireflective hulls of both these Sierpinski objects in the category of $Q$-bitopological spaces turn out to be the category of $T_0$-$Q$-bitopological spaces. We show that only one of these Sierpinski objects is sober $Q$-bitopological space and its epireflective hull in the category of $T_0$-$Q$-bitopological spaces turns out to be the category of saturated $T_{0}$-$Q$-bitopological spaces. | ||
| کلیدواژه‌ها | ||
| $Omega$-algebra؛ $Q$-bitopological space؛ Sierpinski $Q$-bitopological space؛ Sober $Q$-bitopological space؛ $T_0$-$Q$-bitopological space؛ Saturated $T_0$-$Q$-bitopological space؛ Epireflective hull | ||
| مراجع | ||
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[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and Concrete Categories, Wiley, 1990. [2] G. C. L. Brummer, E. Giuli and H. Herrlich, Epireflections which are completions, Cahiers Topo. Geom. Diff. Categoriques, 33 (1992), 71{93. [3] G. Castellini, Closure operators, monomorphisms and epimorphisms in categories of groups, Cahiers Topo. Geom. Diff. Categoriques, 27 (1986), 151{167. [4] E. Giuli and S. Salbany, 2T0 spaces and closure operators, Seminarberichte Fachbereich Math. und Inform., Fern Universitat, Hagen, 29 (1988), 11{40. [5] N. Jacobson, Basic Algebra II, W.H. Freeman and Company, 1980. [6] A. S. Khastgir and A. K. Srivastava, On two epireflective subcategories of the category of 2T0-fuzzy bitopological spaces, Quaest. Math., 23 (2000), 163{177. [7] A. S. Khastgir and A. K. Srivastava, On T0-objects in FTS and BFTS, Fuzzy Sets and Systems, 109 (2000), 301{304. [8] E. G. Manes, Compact Hausdorff objects, General Topology Appl., 4 (1974), 341{360. [9] T. Marny, On epireflective subcategories of topological categories, General Topology Appl., 10 (1979), 175{181. [10] S. E. Rodabaugh, Functorial comparisons of bitopology with topology and the case for redun- dancy of bitopology in lattice-valued mathematics, Appl. Gen. Topol., 9 (2008), 77{108. [11] S. K. Singh and A. K. Srivastava, A characterization of the category Q-TOP, Fuzzy Sets and Systems, 227 (2013), 46{50. [12] S. K. Singh and A. K. Srivastava, On Q-sobriety, Quaest. Math., 39 (2016), 179{188. [13] S. A. Solovyov, Sobriety and spatiality in varieties of algebras, Fuzzy Sets and Systems, 159 (2008), 2567{2585. | ||
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