Connection structures: Grzegorczyk's and Whitehead's definitions of point (Q1355124)

\textit{A. N. Whitehead} [`Process and reality', Macmillan, New York (1929; JFM 55.0035.03)]\ and \textit{A. Grzegorczyk} [Synthese 12, 228-235 (1960; Zbl 0201.32104)]\ independently axiomatized a variant of geometry, in which individual variables are interpreted not as `points', but as `regions'. The primitive relation between regions is the `connection relation', which holds if two regions overlap or have a common boundary point. The authors rephrase the two axiom systems in a common language, and show that, under rather natural additional assumptions, Whitehead's and Grzegorczyk's definitions of `point' define the same object.