Small cardinals and the pseudocompactness of hyperspaces of subspaces of beta omega

Autor(es)

Ortiz-Castillo, Y. F. ^[1] ; Rodrigues, V. O. ^[1] ; Tomita, A. H. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Topology and its Applications; v. 246, p. 9-21, SEP 1 2018.
• Citações Web of Science: 1

Resumo

We study the relations between a generalization of pseudocompactness, named (kappa, M)-pseudocompactness, the countably compactness of subspaces of beta omega and the pseudocompactness of their hyperspaces. We show, by assuming the existence of c-many selective ultrafilters, that there exists a subspace of beta omega that is (kappa, omega{*})-pseudocompact for all kappa < c, but CL(X) is not pseudocompact. We prove in ZFC that if omega subset of X subset of beta omega is such that X is (c, omega{*})-pseudocompact, then CL(X) is pseudocompact, and we further explore this relation by replacing c for some small cardinals. We provide an example of a subspace of beta omega for which all powers below eta are countably compact whose hyperspace is not pseudocompact, we show that if omega subset of X, the pseudocompactness of CL(X) implies that X is (kappa, omega{*})-pseudocompact for all kappa < eta, and provide an example of such an X that is not (b, omega{*})-pseudocompact. (C) 2018 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 16/26216-8 - Topologia e conjuntos
• Beneficiário: Artur Hideyuki Tomita
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 14/16955-2 - Medidas exteriores por seleções fracas e hiperespaços.
• Beneficiário: Yasser Fermán Ortiz Castillo
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 17/15502-2 - Mad Families, Forcing e Princípios Combinatórios em Topologia
• Beneficiário: Vinicius de Oliveira Rodrigues
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