We pose the volume problem for pseudo-Riemannian manifolds and present first results on it: certain geometric properties are read from the volume of small truncated light cones.
Ez, ... be arbitrary non-empty sets and t be a mapping of E into P( U n En), " € 8 2 ?aF"where P(U) denotes the power set of U. Suppose that (~~)~~~, c t ( s ) (
w i t h k c %and with x , € E , for every n c N ' ) and N+%N' imply ( X , ) , €~+ E T ( . ) . Then X = = ( ( E , El, Ez, ...), t ) is called a discrete convergence space and t its discrete convergence. Frequently instead of ( x , , ) , ,~~, c t(.) we write ( x~)~~~ 7 x and say that ( z , )~~ N, converges discretely (to x).
The paper deals-under the viewpoint of topology-with discrete Cauchy spaces, which are spaces where a discrete Cauchy structure (t,C) (with i being a discrete convergence and C being a discrete pre-Cauchy structure) is defined. More precisely, let E 1 , E2 ,... and E be arbitrary sets and let S denote the set of all discrete sequences (x,.
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