On Császár structures and pre-nearness on frames

Abstract

The aim of this paper is to introduce the concept of semi-Császár structures and investigate their relationship with the well-known notion of pre-nearness structures on frames. More explicitly, we define the category of semi-Császár frames and establish a connection with the category of covering pre-nearness frames. We provide conditions under which semi-Császár structures relate with pre-uniformities on frames. Finally, we present a frame counterpart to the relationship between symmetric syntopogenous structures and nearness spaces as established by Herrlich (Gen Topol Appl 4(3):191–212, 1974).