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19 April 2024 |
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The ultrafilter, a peerless tool | | Labib Haddad
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20 Feb 2007 | | Journal: | Tatra Mt. Math. Publ. Density Concepts, 31 (2005) 131--176 | | Subject: | History and Overview; Combinatorics | | Abstract: | This paper was meant for a series of talks at the Bratislava Workshop on the density concept, May 2004. A number of the very many facets of ultrafilters are reviewed (some of them, a bit cursorily, as is to be expected in a short space, and time) including Condorcet’s Paradox, ultraproducts and the theory of infinitesimals (nonstandard analysis), Banach generalized limits in sequence spaces, Choquet’s limits for families of closed sets in general topology and intrinsic geometry, representations of topologies as binary relations among ultrafilters, additive bases in number theory. Peerless indeed, and Protean! | | Source: | arXiv, math/0702587 | | Services: | Forum | Review | PDF | Favorites | |
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