Abstract
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.
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Literatur
Fischer, H. R.: Limesräume. Math. Ann.137, 269–303 (1959).
Cook, C. H., and H. R. Fischer: On equicontinuity and continuous convergence. Math. Ann.159, 94–104 (1965).
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Keller, H.H. Die Limes-Uniformisierbarkeit der Limesräume. Math. Ann. 176, 334–341 (1968). https://doi.org/10.1007/BF02052894
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DOI: https://doi.org/10.1007/BF02052894