Weakly infinite dimensional subsets of R^N

Liljana Babinkostova; Marion Scheepers

Weakly infinite dimensional subsets of R^N

General Topology 2009-01-22 v2

Authors: Liljana Babinkostova , Marion Scheepers

Abstract

The Continuum Hypothesis implies an Erd\"os-Sierpi\'nski like duality between the ideal of first category subsets of $\reals^{\naturals}$ , and the ideal of countable dimensional subsets of $\reals^{\naturals}$ . The algebraic sum of a Hurewicz subset - a dimension theoretic analogue of Sierpinski sets and Lusin sets - of $\reals^{\naturals}$ with any compactly countable dimensional subset of $\reals^{\naturals}$ has first category.

Keywords

set theory and dimension theory set theory topological properties

Cite

@article{arxiv.0811.3661,
  title  = {Weakly infinite dimensional subsets of R^N},
  author = {Liljana Babinkostova and Marion Scheepers},
  journal= {arXiv preprint arXiv:0811.3661},
  year   = {2009}
}

Comments

16 pages, corrected Statements of Theorem 6 and Lemma 8, Inserted Problem 1, Inserted remarks by R. Pol, solving Problem 3, in "Added in Proof" section

Weakly infinite dimensional subsets of R^N

Abstract

Keywords

Cite

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