on continuity and categorical property of interval-valued topological spaces

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.[5] 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 iv-t op. many functors and subcategories of iv-t op are defined and studied. furthermore, the relationships between the iv-t op and its subcategories are investigated. we show that the category t op is isomorphic to the category iv-t op1. moreover, we demonstrate that t op and iv-t op1 are bireflective full subcategories of iv-t op.