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Closed graph property and Khalimsky spaces | ||
| Journal of Finsler Geometry and its Applications | ||
| دوره 6، شماره 1، 2025، صفحه 76-82 اصل مقاله (306.74 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22098/jfga.2025.16485.1145 | ||
| نویسندگان | ||
| Mehrnaz Pourattar1؛ Fatemah Ayatollah Zadeh Shirazi* 2؛ Mohammad Reza Mardanbrigi1 | ||
| 1Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran | ||
| 2Faculty of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran | ||
| چکیده | ||
| In the following text for Khalimsky n-dimensional space Kn we show self-map f:Kn →Kn has closed graph if and only if there exist integers λ1,...,λn such that f is a constant map with value (2λ1,...,2λn). We also show each self--map on Khalimsky circle and Khalimsky sphere which has closed graph is a constant map. The text is motivated by examples. | ||
| کلیدواژه‌ها | ||
| Alexandroff space؛ Closed graph؛ Digital topology؛ Khalimsky spaces | ||
| مراجع | ||
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1. P. Alexandroff, Diskrete R¨aume, Mat. Sb. 2 (1937), 501-518. 2. F. Ayatollah Zadeh Shirazi and N. Golestani, Functional Alexandroff spaces, Hacettepe Journal of Mathematics and Statistics 40/4 (2011), 515-522. 3. F. Ayatollah Zadeh Shirazi and N. Shirinbayan, The size of quasicontinuous maps on Khalimsky line, J. Finsler Geom. Appl. 4 no. 2 (2023), 38-42. 4. T. Banakh, M. Filipczak, and J. W´odka, Returning functions with closed graph are continuous, Mathematica Slovaca, 70 no. 2 (2020), 297-304. 5. R. Berghammer and M. Winter, Order- and graph-theoretic investigation of dimensions of finite topological spaces and Alexandroff spaces, Monatsh. Math. 190 no. 1 (2019),33-78. 6. S.-E. Han, Semi{separation axioms of the infinite Khalimsky topological sphere, Topology Appl. 275 (2020), 107006. 7. S.-E. Han, Sang-Eon, and I.-K. Na, Topologies associated with the one point compactifications of Khalimsky topological spaces, Topology Appl. 241 (2018), 333-344. 8. L. Hol´a and D. Hol´y, Metrizability of the space of quasicontinuous functions, Topology and its Applications 246 (2018), 137-143. 9. G. B. Folland, Real analysis. Modern techniques and their applications, Second edition.Pure and Applied Mathematics, A Wiley-Interscience Publication, John Wiley & Sons,Inc., 1999. 10. T. Husain, The open mapping and closed graph theorems in topological vector spaces,Clarendon Press, Oxford, 1965. 11. E. Khalimsky, R. Kopperman, and P. R. Meyer, Computer graphics and connected topologies on finite ordered sets, Topology Appl. 36 no. 1 (1990), 1-17. 12. V. Krishnamurthy, On the number of topologies on a finite set, American Mathematical Monthly 73/2 (1966), 154-57. 13. J. R. Munkres, Topology A first course, Prentice{Hall Inc., 1975. 14. D. Noll, Topological spaces satisfying a closed graph theorem, Topology Appl. 349 (2024),108903. 15. B. J. Pettis, Closed graph and open mapping theorems in certain topologically complete spaces, Bull. London Math. Soc. 6 (1974), 37-41. 16. L. A. Steen and J. A. Seebach, Counterexamples in topology, Holt, Rinehart and Winston,Inc., 1970. 17. J. H. van der Walt, A closed graph theorem for order bounded operators, Quaest. Math.39 no. 2 (2016), 167-178. | ||
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