Whitehead, in his famous book Process and Reality, proposed a definition of point assuming the concepts of "region" and "connection relation" as primitive. Several years after and independently Grzegorczyk, in a brief but very interesting paper, proposed another definition of point in a system in which the inclusion relation and the relation of being separated were assumed as primitive. In this paper we compare their definitions and we show that, under rather natural assumptions, they coincide.
"Connection Structures: Grzegorczyk's and Whitehead's Definitions of Point." Notre Dame J. Formal Logic 37 (3) 431 - 439, Summer 1996. https://doi.org/10.1305/ndjfl/1039886519