Completeness, Cofinal Completeness And Uniform Paracompactness
In 1915, A paper by E. H. Moore appeared in the Proceedings of the National Academy of Science U.S.A. titled Definition of limit in general integral analysis. This study of unordered summability of sequences led to a theory of convergence by Moore and H. L. Smith titled A general theory of limits which appeared in the American Journal of Mathematics in 1922. In 1937, G. Birkhoff applied the Moore-Smith theory to general topology in an article titled Moore-Smith convergence in general topology, which appeared in the Annals of Mathematics, No. 38, pp. 39-56. In 1940, J. W. Tukey made extensive use of the theory in his monograph titled Convergence and uniformity in topology published in the Annals of Mathematics Studies series. Tukey worked with objects that were generalizations of sequences that he referred to as phalanxes. They were a special case of the objects that are usually called nets today.
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