DENSE METRIZABLE SUBSPACES IN POWERS OF CORSON COMPACTA

Arkady Leiderman; Santi Spadaro; Stevo Todorcevic

doi:10.1090/proc/15885

DENSE METRIZABLE SUBSPACES IN POWERS OF CORSON COMPACTA

Arkady Leiderman, Santi Spadaro, Stevo Todorcevic

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

We characterize when the countable power of a Corson compactum has a dense metrizable subspace and construct consistent examples of Corson compacta whose countable power does not have a dense metrizable subspace. We also give several remarks about ccc Corson compacta and, as a byproduct, we obtain a new proof of Kunen and van Mill's characterization of when a Corson compactum supporting a strictly positive measure is metrizable.

Original language	American English
Pages (from-to)	3177-3187
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	150
Issue number	7
DOIs	https://doi.org/10.1090/proc/15885
State	Published - 1 Jul 2022

Keywords

Corson compactum
Martin's Axiom
countable chain condition
dense metrizable subspace
strictly positive measure

All Science Journal Classification (ASJC) codes

Applied Mathematics
General Mathematics

Access to Document

10.1090/proc/15885

Cite this

@article{768ac9e0af4e4a5694c9e7158a17ebcc,

title = "DENSE METRIZABLE SUBSPACES IN POWERS OF CORSON COMPACTA",

abstract = "We characterize when the countable power of a Corson compactum has a dense metrizable subspace and construct consistent examples of Corson compacta whose countable power does not have a dense metrizable subspace. We also give several remarks about ccc Corson compacta and, as a byproduct, we obtain a new proof of Kunen and van Mill's characterization of when a Corson compactum supporting a strictly positive measure is metrizable.",

keywords = "Corson compactum, Martin's Axiom, countable chain condition, dense metrizable subspace, strictly positive measure",

author = "Arkady Leiderman and Santi Spadaro and Stevo Todorcevic",

note = "Publisher Copyright: {\textcopyright} 2022 American Mathematical Society",

year = "2022",

month = jul,

day = "1",

doi = "10.1090/proc/15885",

language = "American English",

volume = "150",

pages = "3177--3187",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "7",

}

TY - JOUR

T1 - DENSE METRIZABLE SUBSPACES IN POWERS OF CORSON COMPACTA

AU - Leiderman, Arkady

AU - Spadaro, Santi

AU - Todorcevic, Stevo

PY - 2022/7/1

Y1 - 2022/7/1

N2 - We characterize when the countable power of a Corson compactum has a dense metrizable subspace and construct consistent examples of Corson compacta whose countable power does not have a dense metrizable subspace. We also give several remarks about ccc Corson compacta and, as a byproduct, we obtain a new proof of Kunen and van Mill's characterization of when a Corson compactum supporting a strictly positive measure is metrizable.

AB - We characterize when the countable power of a Corson compactum has a dense metrizable subspace and construct consistent examples of Corson compacta whose countable power does not have a dense metrizable subspace. We also give several remarks about ccc Corson compacta and, as a byproduct, we obtain a new proof of Kunen and van Mill's characterization of when a Corson compactum supporting a strictly positive measure is metrizable.

KW - Corson compactum

KW - Martin's Axiom

KW - countable chain condition

KW - dense metrizable subspace

KW - strictly positive measure

UR - http://www.scopus.com/inward/record.url?scp=85130984709&partnerID=8YFLogxK

U2 - 10.1090/proc/15885

DO - 10.1090/proc/15885

M3 - Article

SN - 0002-9939

VL - 150

SP - 3177

EP - 3187

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 7

ER -

DENSE METRIZABLE SUBSPACES IN POWERS OF CORSON COMPACTA

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this