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An approach to change the topology of a topological space with the help of its closed sets in the presence of grills | ||
| Journal of Mahani Mathematical Research | ||
| دوره 10، شماره 2، دی 2021، صفحه 9-19 اصل مقاله (470.03 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmrc.2021.17094.1132 | ||
| نویسنده | ||
| Amin Talabeigi* | ||
| Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| چکیده | ||
| The aim of this paper is introduce an approach to convert the topology of a topological space to another topology(in fact, a coarser topology). For this purpose, considering a closed set P of subsets of a topological space (X; T) and a grill G on the space, we use the closure operator cl associated with T, to define a new Kuratowski closure operator cl_p on X. The operator cl_p induces the desired topology. We then characterize the form of this resulting topology and also determine its relationship to the initial topology of the space. Some examples are given. Also, using a suitable grill in the method, we convert each topological space to corresponding D-space. | ||
| کلیدواژهها | ||
| Kuratowski closure operator؛ Kuratowski closure axioms؛ grill؛ D-topology؛ D-space | ||
| مراجع | ||
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A. Talabeigi, On the Tychonoff's type theorem via grills, Bull. Iranian Math. Soc., Vol. 42, No. 1 (2016), 37-41.
A. Talabeigi, Extracting some supra topologies from the topology of a topological space using stacks(Accepted in AUT Journal of Mathematics and Computing (AJMC) and to appear). doi: 10.22060/ajmc.2021.19123.1042
W. J. Thron, Proximity structures and grills, Math. Ann. Vol. 206, (1973), 35-62.
S. Willard, General topology, Addison–Wesley publishing company, 1970. | ||
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