On powers of countably pracompact groups

Autor(es)

Tomita, Artur Hideyuki ; Trianon-Fraga, Juliane

• Tipo de documento: Artigo Científico
• Fonte: Topology and its Applications; v. 327, p. 31-pg., 2023-02-02.

Resumo

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)

• Processo FAPESP: 21/00177-4 - Espaços topológicos e conjuntos
• Beneficiário: Artur Hideyuki Tomita
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 19/12628-0 - Pseudocompacidade e ultrafiltros
• Beneficiário: Juliane Trianon Fraga
• Modalidade de apoio: Bolsas no Brasil - Doutorado