On powers of countably pracompact groups
Artur Hideyuki Tomita, Juliane Trianon-Fraga

TL;DR
This paper constructs examples of topological groups with specific countably pracompact properties at certain powers, assuming the existence of multiple incomparable selective ultrafilters, addressing a question posed by Comfort in 1990.
Contribution
The paper provides the first constructions of topological groups with prescribed countably pracompact powers at certain cardinals, under set-theoretic assumptions.
Findings
Constructs groups with countably pracompact powers at = \, \u03ba^+ for = , , assuming selective ultrafilters.
Shows existence of groups where the -th power is countably pracompact but the next power is not.
Addresses a longstanding question about the behavior of countably pracompact powers in topological groups.
Abstract
In 1990, Comfort asked: is there, for every cardinal number , a topological group such that is countably compact for all cardinals , but is not countably compact? A similar question can also be asked for countably pracompact groups: for which cardinals is there a topological group such that is countably pracompact for all cardinals , but is not countably pracompact? In this paper we construct such group in the case , assuming the existence of incomparable selective ultrafilters, and in the case , with , assuming the existence of incomparable selective ultrafilters. In particular, under the second assumption, there exists a topological group so…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Mathematical and Theoretical Analysis
