Interor and h operators on the category of locales

Abstract

We present the concept of interior operator $I$ on the category $\mathbf{Loc}$ of locales and then we construct a topological category \linebreak $(\mathbf{I}\text{-}\mathbf{Loc},U)$, where $U:\mathbf{I}\text{-}\mathbf{Loc}\to \mathbf{Loc}$ is a forgetful functor; and we also introduce the notion of $\mathfrak{h}$ operator on the category $\mathbf{Loc}$ and discuss some of their properties for constructing the topological category $(\mathfrak{h}\text{-}\mathbf{Loc},U)$ associated to the forgetful functor $U:\mathfrak{h}\text{-}\mathbf{Loc}\to \mathbf{Loc}$.

arXiv commentarXiv admin note: text overlap with arXiv:2010.05284 by other authors