Die Limes-Uniformisierbarkeit der Limesräume

Convergence structures (Limitierungen) defined by H. R. Fischer [1] in 1959 anduniform convergence structures (uniforme Limitierungen) introduced by C. H. Cook and H. R. Fischer [2] in 1965 are generalizations of the concepts of topology and uniformity respectively. A convergence structure, induced by some uniform convergence structure, will be called (L)-uniformizable (Limes-uniformisierbar). In this paper a necessary and sufficient condition for (L)-uniformizability of a convergence structure will be given. As a consequence any separated (Hausdorff) convergence structure on a set turns out to be (L)-uniformizable. Also any compatible convergence structure (separated or not) on a group is (L)-uniformizable.