Skip to main content
Topology and its ApplicationsVolume 305, 1 January 2022, Article number 107872

Maximal almost disjoint families and pseudocompactness of hyperspaces(Article)(Open Access)

  Save all to author list
  • aCentro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Campus Morelia, Morelia, Michoacán 58089, Mexico
  • bInstitute of Mathematics and Statistics, University of São Paulo, Rua do Matão, São Paulo, 1010, Brazil
  • cDepartment of Mathematics, University of Toronto, Toronto, ON M5S 2E4, Canada

Abstract

We show that all Ψ-spaces associated to maximal almost disjoint families have pseudocompact Vietoris hyperspace if and only if MAc(P(ω)/fin) holds. We further study the question whether there is a maximal almost disjoint family whose hyperspace is pseudocompact and construct a consistent example of a maximal almost disjoint family of size ω2<c whose hyperspace is not pseudocompact. © 2021 Elsevier B.V.

Author keywords

Almost disjoint familyPseudocompact spaceVietoris hyperspace

Funding details

Funding sponsor Funding number Acronym
Fundação de Amparo à Pesquisa do Estado de São Paulo
See opportunities by FAPESP		FAPESP
Consejo Nacional de Ciencia y TecnologíaA1-S-16164CONACYT

  • 1

    The research of the second author was supported by a PAPIIT grants IN100317, IN104220 and CONACYT grant A1-S-16164.The third author received support from FAPESP (grants 2017/15502-2 and 2019/01388-9. He was also a visiting scholar at the Fields Institute for Mathematical Research while this work was being made.The fourth author is partially supported by Grants from NSERC (455916) and CNRS (IMJ-PRG UMR7586).The fifth author received support from FAPESP (grant 2019/19924-4).

  • ISSN: 01668641
  • CODEN: TIAPD
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1016/j.topol.2021.107872
  • Document Type: Article
  • Publisher: Elsevier B.V.

  Hrušák, M.; Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Campus Morelia, Morelia, Michoacán, Mexico;
© Copyright 2021 Elsevier B.V., All rights reserved.

Cited by 2 documents

Corral, C. , de O. Rodrigues, V.
New examples of MAD families with pseudocompact hyperspaces
(2024) Topology and its Applications
Corral, C. , Rodrigues, V.O.
Fin-intersecting MAD families
(2024) Filomat
View details of all 2 citations
Inform me when this document is cited in Scopus:
Set citation alert Set citation feed
{"topic":{"name":"Ultrafilter; Covering Property; Number","id":10534,"uri":"Topic/10534","prominencePercentile":72.6107,"prominencePercentileString":"72.611","overallScholarlyOutput":0},"dig":"61ef9f5cfc96d292901d1e5b62d8a02954c7adbe55a7065d1193adb0aa39ba4d"}

SciVal Topic Prominence

Topic:
Prominence percentile: