Resolvability vs. almost resolvability

István Juhász; Saharon Shelah; Lajos Soukup

doi:10.1016/j.topol.2009.03.019

Resolvability vs. almost resolvability

István Juhász^*
, Saharon Shelah
, Lajos Soukup

^*Corresponding author for this work

Einstein Institute of Mathematics

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

2 Scopus citations

Abstract

A space X is κ-resolvable (resp. almost κ-resolvable) if it contains κ dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subsets of X). Answering a problem raised by Juhász, Soukup, and Szentmiklóssy, and improving a consistency result of Comfort and Hu, we prove, in ZFC, that for every infinite cardinal κ there is an almost 2^κ-resolvable but not ω₁-resolvable space of dispersion character κ.

Original language	English
Pages (from-to)	1966-1969
Number of pages	4
Journal	Topology and its Applications
Volume	156
Issue number	11
DOIs	https://doi.org/10.1016/j.topol.2009.03.019
State	Published - 15 Jun 2009

Keywords

Almost κ-resolvable space
Extraresolvable space
κ-Resolvable space

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10.1016/j.topol.2009.03.019

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title = "Resolvability vs. almost resolvability",

abstract = "A space X is κ-resolvable (resp. almost κ-resolvable) if it contains κ dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subsets of X). Answering a problem raised by Juh{\'a}sz, Soukup, and Szentmikl{\'o}ssy, and improving a consistency result of Comfort and Hu, we prove, in ZFC, that for every infinite cardinal κ there is an almost 2κ-resolvable but not ω1-resolvable space of dispersion character κ.",

keywords = "Almost κ-resolvable space, Extraresolvable space, κ-Resolvable space",

author = "Istv{\'a}n Juh{\'a}sz and Saharon Shelah and Lajos Soukup",

year = "2009",

month = jun,

day = "15",

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language = "אנגלית",

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T1 - Resolvability vs. almost resolvability

AU - Juhász, István

AU - Shelah, Saharon

AU - Soukup, Lajos

PY - 2009/6/15

Y1 - 2009/6/15

N2 - A space X is κ-resolvable (resp. almost κ-resolvable) if it contains κ dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subsets of X). Answering a problem raised by Juhász, Soukup, and Szentmiklóssy, and improving a consistency result of Comfort and Hu, we prove, in ZFC, that for every infinite cardinal κ there is an almost 2κ-resolvable but not ω1-resolvable space of dispersion character κ.

AB - A space X is κ-resolvable (resp. almost κ-resolvable) if it contains κ dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subsets of X). Answering a problem raised by Juhász, Soukup, and Szentmiklóssy, and improving a consistency result of Comfort and Hu, we prove, in ZFC, that for every infinite cardinal κ there is an almost 2κ-resolvable but not ω1-resolvable space of dispersion character κ.

KW - Almost κ-resolvable space

KW - Extraresolvable space

KW - κ-Resolvable space

UR - https://www.scopus.com/pages/publications/67349165562

U2 - 10.1016/j.topol.2009.03.019

DO - 10.1016/j.topol.2009.03.019

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AN - SCOPUS:67349165562

SN - 0166-8641

VL - 156

SP - 1966

EP - 1969

JO - Topology and its Applications

JF - Topology and its Applications

IS - 11

ER -

Resolvability vs. almost resolvability

Abstract

Keywords

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