A tall space with a small bottom

István Juhász; Saharon Shelah; Lajos Soukup; Zoltán Szentmiklóssy

doi:10.1090/s0002-9939-03-06662-0

A tall space with a small bottom

István Juhász^*
, Saharon Shelah
, Lajos Soukup
, Zoltán Szentmiklóssy

^*Corresponding author for this work

Einstein Institute of Mathematics

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

5 Scopus citations

Abstract

We introduce a general method of constructing locally compact scattered spaces from certain families of sets and then, with the help of this method, we prove that if κ^<κ = κ, then there is such a space of height κ⁺ with only κ many isolated points. This implies that there is a locally compact scattered space of height ω₂ with ω₁ isolated points in ZFC, solving an old problem of the first author.

Original language	English
Pages (from-to)	1907-1916
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	131
Issue number	6
DOIs	https://doi.org/10.1090/s0002-9939-03-06662-0
State	Published - Jun 2003

Keywords

Locally compact scattered space
Superatomic Boolean algebra

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10.1090/s0002-9939-03-06662-0

Cite this

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abstract = "We introduce a general method of constructing locally compact scattered spaces from certain families of sets and then, with the help of this method, we prove that if κ<κ = κ, then there is such a space of height κ+ with only κ many isolated points. This implies that there is a locally compact scattered space of height ω2 with ω1 isolated points in ZFC, solving an old problem of the first author.",

keywords = "Locally compact scattered space, Superatomic Boolean algebra",

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AB - We introduce a general method of constructing locally compact scattered spaces from certain families of sets and then, with the help of this method, we prove that if κ<κ = κ, then there is such a space of height κ+ with only κ many isolated points. This implies that there is a locally compact scattered space of height ω2 with ω1 isolated points in ZFC, solving an old problem of the first author.

KW - Locally compact scattered space

KW - Superatomic Boolean algebra

UR - https://www.scopus.com/pages/publications/0037725104

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A tall space with a small bottom

Abstract

Keywords

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