On a model for non commutative geometric spaces
The author proposes a model for non-commutative geometries, which allows to describe axioms by corresponding equations. The article constitutes the basis for further developments, although some first hand applications are made here, mainly to the theory previously developed by J. André et al. [cf. for example, \textit{J. André}, Geom. Dedicata 13, 351-360 (1983; Zbl 0515.05017)]. In the present article the author departs from a triple \((X,<,>,R),\) called non commutative geometric space, where X, R are non- empty sets and \(<,>: X^ 2\to R\) is a map. X is thought as the set of ''points'', the image of \(<,>\) being the set of directions (Richtungen) or ideal points (Fernpunkte) and \(<,>\) being called the ''parallel map''. Suitable axioms are introduced and their behaviour under morphisms is described. Further applications to group spaces are promised.
scientific article; zbMATH DE number 3929831