By Werner Haupt
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Extra resources for German Anti-Tank Guns: 37Mm, 50Mm, 75Mm, 88Mm Pak, 1935-1945 : Without Self-Propelled Mountings
Example text
Now introduce, for every x EX Dx = {A: x E A'}. Then (0:), ({3), ('"'() are equivalent to the very simple statement: for all x E X, Dx is a grill and consists only of non-principal ultrafilters. Dx = 0 is possible. If Dx i- 0 Riesz called x a principal element. We shall call Dx the cluster grill at x. Hilbert had introduced a spatial structure in terms of neighborhoods in 1902. Riesz realized that, (Dx) is a family of neighborhoods. In our terminology ,(Dx) is the filter of deleted neighborhoods.
Teaching; the Moore method . . . . . . . . . . . . . . . . . Acknowledgements. . . . . . . . . . . . . . . . . . . . . E. Aull and R. ), Handbook of the History of General Topology, Volume 1, 41-61. © 1997 Kluwer Academic Publishers. SOME ASPECTS OF THE WORK AND INFLUENCE OF R. L. MOORE 43 Introduction There is a considerable body of literature dealing largely or in part with the life, work, teaching, influence, and legacy of R. L. Moore. This article will supply for the interested reader a list of such writings.
So Vietoris develops in parallel today's theory of convergence for generalized set sequences (nets) and filter bases through comparison with the directed set of neighbourhoods. After G. Birkhoff reinvented the filter base notion in 1935 [4], J. Schmidt wrote in his 1953 work "Beitrage zur Filtertheorie II"(dedicated to Prof. Vietoris) [16], but without mentioning that also directed sets and nets can already be found in Vietoris [24]: "The history of the filter obviously shows features similar to other human inventions.