Infinite dimensions for ordered incidence geometry (Q1262529)

In J. Geom. 30, 103-122 (1988; Zbl 0629.51013), \textit{A. Ben-Tal} and \textit{A. Ben-Israel} have set up an abstract conexity theory based on the notions of incidence, order, affine hull and dimension. Although they incorporate the case of infinite dimensions into their axiomatic setting, their work mainly refers to finite dimensional geometries and seems to need some refinements as for the infinite dimensional case. This is done in the paper under review. By a few minor modifications to the axioms and to the results, the author establishes Ben-Tal's and Ben-Israel's theory for arbitrary dimensions. In particular, he gives a version of the hyperplane separation theorem for infinite dimensional ordered incidence geometries.