On continuity and categorical property of interval-valued topological spaces

Document Type : Research Paper


1 Computer Science Department, Cihan University-Erbil, Kurdistan Region, Iraq

2 Department of Mathematics, Hodeidah University-Hodeidah, Yemen

3 Department of Mathematics, Women Section, King Saud University, Riyadh 12372, KSA


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 $\mathcal{IV}$-$\mathcal{TOP}$.


Articles in Press, Corrected Proof
Available Online from 07 February 2023
  • Receive Date: 16 November 2022
  • Revise Date: 25 December 2022
  • Accept Date: 26 January 2023
  • First Publish Date: 07 February 2023