Document Type : Original Manuscript


1 Department of Basic Sciences, Birjand University of Technology, P.O. Box 226, Birjand, Iran.

2 Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.


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.


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