On powers of countably pracompact groups

Author(s)

Tomita, Artur Hideyuki ; Trianon-Fraga, Juliane

• Document type: Journal article
• Source: Topology and its Applications; v. 327, p. 31-pg., 2023-02-02.

Abstract

In 1990, Comfort asked: is there, for every cardinal number alpha < 2c, a topological group G such that G gamma is countably compact for all cardinals -y < alpha, but G alpha is not countably compact? A similar question can also be asked for countably pracompact groups: for which cardinals alpha is there a topological group G such that G gamma is countably pracompact for all cardinals -y < alpha, but G alpha is not countably pracompact? In this paper we construct such group in the case alpha = w, assuming the existence of c incomparable selective ultrafilters, and in the case alpha = iota c+, with w < iota c < 2c, assuming the existence of 2c incomparable selective ultrafilters. In particular, under the second assumption, there exists a topological group G so that G2c is countably pracompact, but G(2c)+ is not countably pracompact, unlike the countably compact case. (AU)

• FAPESP's process: 21/00177-4 - Topological spaces and set Theory
• Grantee: Artur Hideyuki Tomita
• Support Opportunities: Regular Research Grants
• FAPESP's process: 19/12628-0 - Pseudocompactness and ultrafilters
• Grantee: Juliane Trianon Fraga
• Support Opportunities: Scholarships in Brazil - Doctorate