Weakly infinite dimensional subsets of R{double-struck}N{double-struck}

Liljana Babinkostova; Marion Scheepers

doi:10.1016/j.topol.2009.03.058

Weakly infinite dimensional subsets of R{double-struck}^{N{double-struck}}

Liljana Babinkostova, Marion Scheepers

Mathematics Department

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

3 Scopus citations

Abstract

The Continuum Hypothesis implies an Erdös-Sierpiński like duality between the ideal of first category subsets of R{double-struck}^{N{double-struck}}, and the ideal of countable dimensional subsets of R{double-struck}^{N{double-struck}}. The algebraic sum of a Hurewicz subset - a dimension theoretic analogue of Sierpiński sets and Lusin sets - of R{double-struck}^{N{double-struck}} with any compactly.

Original language	English
Pages (from-to)	1302-1313
Number of pages	12
Journal	Topology and its Applications
Volume	157
Issue number	8
DOIs	https://doi.org/10.1016/j.topol.2009.03.058
State	Published - Jun 2010

Keywords

Classes of open covers
Countable dimensional
Hurewicz sets
N-dimensional
Selection principles
Weakly infinite dimensional

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10.1016/j.topol.2009.03.058

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title = "Weakly infinite dimensional subsets of R\{double-struck\}N\{double-struck\}",

abstract = "The Continuum Hypothesis implies an Erd{\"o}s-Sierpi{\'n}ski like duality between the ideal of first category subsets of R\{double-struck\}N\{double-struck\}, and the ideal of countable dimensional subsets of R\{double-struck\}N\{double-struck\}. The algebraic sum of a Hurewicz subset - a dimension theoretic analogue of Sierpi{\'n}ski sets and Lusin sets - of R\{double-struck\}N\{double-struck\} with any compactly.",

keywords = "Classes of open covers, Countable dimensional, Hurewicz sets, N-dimensional, Selection principles, Weakly infinite dimensional",

author = "Liljana Babinkostova and Marion Scheepers",

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AU - Scheepers, Marion

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N2 - The Continuum Hypothesis implies an Erdös-Sierpiński like duality between the ideal of first category subsets of R{double-struck}N{double-struck}, and the ideal of countable dimensional subsets of R{double-struck}N{double-struck}. The algebraic sum of a Hurewicz subset - a dimension theoretic analogue of Sierpiński sets and Lusin sets - of R{double-struck}N{double-struck} with any compactly.

AB - The Continuum Hypothesis implies an Erdös-Sierpiński like duality between the ideal of first category subsets of R{double-struck}N{double-struck}, and the ideal of countable dimensional subsets of R{double-struck}N{double-struck}. The algebraic sum of a Hurewicz subset - a dimension theoretic analogue of Sierpiński sets and Lusin sets - of R{double-struck}N{double-struck} with any compactly.

KW - Classes of open covers

KW - Countable dimensional

KW - Hurewicz sets

KW - N-dimensional

KW - Selection principles

KW - Weakly infinite dimensional

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SN - 0166-8641

VL - 157

SP - 1302

EP - 1313

JO - Topology and its Applications

JF - Topology and its Applications

IS - 8

ER -

Weakly infinite dimensional subsets of R{double-struck}^{N{double-struck}}

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Keywords

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