Weakly Infinite Dimensional Subsets of RN

Liljana Babinkostova; Marion Scheepers

Weakly Infinite Dimensional Subsets of R^N

Liljana Babinkostova, Marion Scheepers

Mathematics Department

Boise State University

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

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Abstract

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

Original language	American English
Journal	Topology and its Applications
State	Published - 1 Jun 2010

Keywords

classes of open covers
countable dimensional
n-dimensional
selection principles

EGS Disciplines

Mathematics

Access to Document

Weakly Infinite Dimensional Subsets of R sup N sup Final published version, 505 KBLicense: Unspecified

Cite this

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

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T1 - Weakly Infinite Dimensional Subsets of RN

AU - Babinkostova, Liljana

AU - Scheepers, Marion

PY - 2010/6/1

Y1 - 2010/6/1

N2 - The Continuum Hypothesis implies an Erdö-Sierpiński like duality between the ideal of first category subsets of ℝℕ, and the ideal of countable dimensional subsets of ℝℕ. The algebraic sum of a Hurewicz subset - a dimension theoretic analogue of Sierpinski sets and Lusin sets - of ℝℕ with any compactly countable dimensional subset of ℝℕ has first category.

AB - The Continuum Hypothesis implies an Erdö-Sierpiński like duality between the ideal of first category subsets of ℝℕ, and the ideal of countable dimensional subsets of ℝℕ. The algebraic sum of a Hurewicz subset - a dimension theoretic analogue of Sierpinski sets and Lusin sets - of ℝℕ with any compactly countable dimensional subset of ℝℕ has first category.

KW - classes of open covers

KW - countable dimensional

KW - n-dimensional

KW - selection principles

UR - https://scholarworks.boisestate.edu/math_facpubs/25

M3 - Article

SN - 0016-660X

JO - Topology and its Applications

JF - Topology and its Applications

ER -