2007/10/12 by Daniel Litt, Zachary Abel, Litt, Daniel +3
Computer Science · Mathematics · #16B50 (Secondary) #54D80 (Primary) #Advanced Topology and Set Theory #Category Theory (math.CT) #Computability, Logic, AI Algorithms #FOS: Mathematics #General Mathematics (math.GM) #General Topology (math.GN) #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.0710.2497
openalex publication_date 2007/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.