On quasiaffine spaces and coherent configurations

In 2] André deduced a (1?1) correspondence between the class of homogeneous coherent configurations and the class of certain noncommutative spaces which he called quasiaffine. In this note we establish a (1?1) correspondence between (not necessarily homogeneous) coherent configurations and weakly quasiaffine spaces which generalizes André's. Furthermore we consider some applications of this correspondence to quasiaffine spaces; especially we characterize such spaces with maximal diameter with respect to one direction (compare with 5]).