On Nets and Filters.

Abstract

In the theory of convergence classes as described in [...] four axioms are needed, while the corresponding filter version only needs three. Yet there is a natural correspondence between the filter axioms and three of the next axioms. On the basis of this E. M. Alfsen raised the question whether the fourth net axiom could be deduced from the three other ones. After a suitable adjustment of the definition of subnet this is indeed the case. In this paper we give a definition of subnet which meets this purpose. In addition we shall take time to remove some irregularities concerning nets and subsets.