Bounded nets in preseminormed spaces (Q1192296)

By using preseminormed spaces instead of topological vector spaces, we introduce a reasonable new notion of bounded nets under which each Cauchy net becomes bounded. And after some preparations, we show that bounded nets and null nets can be characterized in terms of each other. Moreover, by identifying sets with nets in a natural way, we obtain standard theorems on bounded sets as very particular cases of our results.