El Instituto Jorge Juan del CSIC posteriormente se integraría en el Instituto de Matemáticas y Física Fundamental (IMAFF).D.W. Curtis and J.C. Matthews have introduced some structures which generalize, to the product of two sets, structures of usual uniform types. However, their axiomatic is not very natural and, in general, it makes no reference to filters. J.M. Gracia and V.M. Onieva introduce an axiomatic inspired in Cutis' and Matthews', which reflects the generalization in a natural way, presenting the structures of the first authors within their framework. In this note, we essentially characterize the topologies which are compatible with the structures of [7] and we examine the regularity axioms of A.S. Davis in relation with these structures, refining or completing several results of [2], [8].Peer reviewed