On a definition of simultaneity and distance

The possibility to formulate a special relativity based on the generalization of the concept of simultaneity has been previously discussed. The indicated generalization practically consists in the substitution, in special Lorentz transformations, of the time coordinate t for the t+(2epsilonsub(0)-1)csup(-1) x, where 0 < epsilonsub(0) < 1 (epsilonsub(0)=1/2 corresponds to the traditional definition of simultaneity). The transformations obtained in such a way (generalized Lorentz transformations) provided the quadratic form invariance rsup(2)=gsub(ik)xsub(i)xsub(k) (i,k=0, 1; x0=t; x1=x), where gsub(ik) is a constant metric tensor with components gsub(00)=1, gsub(01)=(2epsilonsub(0)-1)csup(-1), gsub(11)=4epsilonsub(0)(epsilonsub(0)-1)csup(-2). The possibility is considered of that in the known formula which defines the distance between points A and B, Xsub(AB)=epsilonsub(1)c(tsub(2)-tsub(1)), where tsub(1) is the time of sending a light signal from A to B and tsub(2) is the time of its return to A after reflecting at B; epsilon1 can be equal to 0 < epsilon1 < 1, not necessarily to 1/2. It is shown that the assumption connected with a possible space anisotropy is inconsistent (if epsilon1 not equal to 1/2) with a necessary condition of the invariance of the light propagation equations