%0 Journal Article
%T On continuity and categorical property of interval-valued topological spaces
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Saleh, S.
%A Al-Mufarrij, Jawaher
%A Nahi Alrabeeah, Abdullah Abdulabbas
%D 2023
%\ 09/01/2023
%V 14
%N 9
%P 385-392
%! On continuity and categorical property of interval-valued topological spaces
%K $IV$-sets
%K $IV$-topology
%K $IV$-product
%K $IV$-continuous maps
%K Category theory
%R 10.22075/ijnaa.2023.29326.4241
%X 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 $\mathcal{IV}$-$\mathcal{TOP}$.
%U https://ijnaa.semnan.ac.ir/article_7412_11877e6fd110247b7e5f9ef0c5b4862f.pdf