c_L-regular-open and c_L-regular-closed elements by clouser function in pointfree topology

In this paper, we consider the pairs (L,\mathrm{cl}_L), whereL is a locale and \mathrm{cl}_L\colon L\rightarrow Lis a closure function on L and alsodescribe connections between closure functions and interior functions in a locale L.Moreover, we introduce c_L-regular-open and c_L-regular-closed elements in a closure function andstudy their fundamental properties. We show that the set of all c_L-regular-open elements and c_L-regular-closed elements in locale L are frames with binary relation \leq_L.

کلیدواژه ها:

locale ، isotonic space ، c_L-regular-closed element ، c_L-regular-open element