ISOTONIC CLOSURE FUNCTIONS ON A LOCALE | ||
| Journal of Algebraic Systems | ||
| دوره 11، شماره 2، فروردین 2024، صفحه 13-32 اصل مقاله (191.88 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.12101.1627 | ||
| نویسندگان | ||
| Toktam Haghdadi* 1؛ Ali Akbar Estaji2 | ||
| 1Department of Basic Sciences, Birjand University of Technology, P.O. Box 226, Birjand, Iran. | ||
| 2Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran. | ||
| چکیده | ||
| In this paper, we introduce and study isotonic closure functions on a locale. These are pairs of the form $(L, \underline{{\mathrm{cl}}}_L)$, where $L$ is a locale and $\underline{{\mathrm{cl}}}_L\colon \mathcal{S}\!\ell(L) \rightarrow \mathcal{S}\!\ell(L)$ is an isotonic closure function on the sublocales of $L$. Moreover, we introduce generalized $\underline{{\mathrm{cl}}}_L$- closed sublocales in isotonic closure locales and discuss some of their properties. Also, we introduce and study the category $ \textbf{ICF} $ whose objects and morphisms are isotonic closure functions $(L, \underline{{\mathrm{cl}}}_L)$ and localic maps, respectively. | ||
| کلیدواژهها | ||
| Isotonic closure function؛ Locale؛ Neighborhood function؛ Category | ||
| مراجع | ||
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