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LG-paracompactness of LG-fuzzy topological metric spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 25، دوره 15، شماره 1، فروردین 2024، صفحه 313-320 اصل مقاله (399.71 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23018.2456 | ||
| نویسنده | ||
| Marzieh Mostafavi* | ||
| Department of Mathematics, Faculty of Basic Sciences, University of Qom, Qom, Iran. | ||
| تاریخ دریافت: 10 فروردین 1400، تاریخ بازنگری: 15 تیر 1400، تاریخ پذیرش: 30 مرداد 1400 | ||
| چکیده | ||
| In this manuscript, we introduce $LG^{c}$-fuzzy Euclidean topological space in which $L$ denotes a completely distributive lattice with a countable subset dense in it. We use the structure of $LG$-fuzzy topological space $(X,\ \mathfrak{T})$, which $X$ is an $L$-fuzzy subset of the crisp set $M$ and $\mathfrak{T}: L^M_X \to L $, is an $L$-gradation of openness on $X$ to define the fundamental concepts of $LG$-fuzzy analysis such as $LG$-locally compactness and $LG$-paracompactness and prove several theorems. In consequence, we show that any second countable Hausdorff $LG$-fuzzy topological space that is $LG$-locally compact is $LG$-paracompact. Also from any given metric $\rho$ on a crisp set $M$ and $L$-fuzzy subset $X$ of it, we construct an $L$-gradation of openness $\mathfrak{T}_{\rho}$ on $X$ and obtain $LG$-fuzzy topological metric space $(X,\mathfrak{T}_{\rho} )$. Finally, we prove an interesting theorem: Every $LG$-fuzzy topological metric space, is $LG$-paracompact. | ||
| کلیدواژه‌ها | ||
| $LG^{c}$-fuzzy Euclidean topological space؛ $LG$-locally compact؛ $LG$-fuzzy topological metric space؛ }{ $LG$-paracompact | ||
| مراجع | ||
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