The ultrafilter, a peerless tool

Details The ultrafilter, a peerless tool The ultrafilter, a peerless tool

2007-02-20

arxiv.org/abs/math/0702587v1

Tatra Mt. Math. Publ. Density Concepts, 31 (2005) 131--176

Mathematics

History and Overview

With the permission of Professor Duchon, editor in chief, and Professor Nemoga, managing editor, Tatra Mt. Publ

Scientific paper

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!

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