%0 Journal Article %T ISOTONIC CLOSURE FUNCTIONS ON A LOCALE %J Journal of Algebraic Systems %I Shahrood University of Technology %Z 2345-5128 %A Haghdadi, Toktam %A Estaji, Ali Akbar %D 2024 %\ 01/01/2024 %V 11 %N 2 %P 13-32 %! ISOTONIC CLOSURE FUNCTIONS ON A LOCALE %K Isotonic closure function %K Locale %K Neighborhood function %K Category %R 10.22044/jas.2022.12101.1627 %X In this paper, we introduce and study isotonic closure functions on a locale. These are pairs of the form $(L, \underline{{\mathrm{cl}}}_L)$, where$L$ is a locale and $\underline{{\mathrm{cl}}}_L\colon \mathcal{S}\!\ell(L) \rightarrow \mathcal{S}\!\ell(L)$is an isotonic closure function on the sublocales of $L$. Moreover, we introduce generalized$\underline{{\mathrm{cl}}}_L$- closed sublocales in isotonic closure locales and discuss some of their properties. Also, we introduce and study the category $ \textbf{ICF} $ whose objects and morphisms are isotonic closure functions $(L, \underline{{\mathrm{cl}}}_L)$ and localic maps, respectively. %U https://jas.shahroodut.ac.ir/article_2728_9048642dc8c7868e1956de9b20810e1e.pdf