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On continuity and categorical property of interval-valued topological spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 29، دوره 14، شماره 9، آذر 2023، صفحه 385-392 اصل مقاله (373.9 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29326.4241 | ||
| نویسندگان | ||
| S. Saleh* 1، 2؛ Jawaher Al-Mufarrij3؛ Abdullah Abdulabbas Nahi Alrabeeah1 | ||
| 1Computer Science Department, Cihan University-Erbil, Kurdistan Region, Iraq | ||
| 2Department of Mathematics, Hodeidah University-Hodeidah, Yemen | ||
| 3Department of Mathematics, Women Section, King Saud University, Riyadh 12372, KSA | ||
| تاریخ دریافت: 25 آبان 1401، تاریخ بازنگری: 04 دی 1401، تاریخ پذیرش: 06 بهمن 1401 | ||
| چکیده | ||
| An interval set (or an interval-valued set), is a special set, which is an effective tool for illustrating and describing obscure information systems and partially known problems. Recently, Kim et al.\cite{r5} defined the topological structure for interval-value sets and studied many properties of them. In this work, we discuss some characteristics and relations of continuity in interval-valued topological spaces with some necessary illustrative examples. Then we provide a categorical framework for interval-valued topological spaces $\mathcal{IV}$-$\mathcal{TOP}$. Many functors and subcategories of $\mathcal{IV}$-$\mathcal{TOP}$ are defined and studied. Furthermore, the relationships between the $\mathcal{IV}$-$\mathcal{TOP}$ and its subcategories are investigated. We show that the category $\mathcal{TOP}$ is isomorphic to the category $\mathcal{IV}$-${\mathcal{TOP}_{1}}.$ Moreover, we demonstrate that $\mathcal{TOP}$ and $\mathcal{IV}$-$\mathcal{TOP}_{1}$ are bireflective full subcategories of $\mathcal{IV}$-$\mathcal{TOP}$. | ||
| کلیدواژه‌ها | ||
| $IV$-sets؛ $IV$-topology؛ $IV$-product؛ $IV$-continuous maps؛ Category theory | ||
| مراجع | ||
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