A Categorical Construction of Ultrafilters
Category Theory
2009-05-13 v2 General Mathematics
General Topology
Abstract
Ultrafilters are useful mathematical objects having applications in nonstandard analysis, Ramsey theory, Boolean algebra, topology, and other areas of mathematics. In this note, we provide a categorical construction of ultrafilters in terms of the inverse limit of an inverse family of finite partitions; this is an elementary and intuitive presentation of a consequence of the profiniteness of Stone spaces. We then apply this construction to answer a question of Rosinger posed in arXiv:0709.0084v2 in the negative.
Keywords
Cite
@article{arxiv.0710.2497,
title = {A Categorical Construction of Ultrafilters},
author = {Daniel Litt and Zachary Abel and Scott D. Kominers},
journal= {arXiv preprint arXiv:0710.2497},
year = {2009}
}
Comments
5 pages