On Hurewicz subsets of a countable power of the real line.
by
Marion Scheepers
Boise State University
Coauthors: Liljana Babinkostova

Hurewicz sets are in spaces of infinite covering dimension the of analogue for the ideal zerodimensional subsets of Sierpinski sets for Lebesgue measure zero sets of reals, and of Lusin sets for first category sets of reals. Hurewicz showed in the 1920s that existence of Hurewicz sets is equivalent to the Continuum Hypothesis. This is analogous to Rothberger's classical result that the simultaneous existence of a Lusin set and a Sierpinski set is equivalent to the Continuum Hypothesis.

We point out another very suggestive analogue between properties of Hurewicz sets and Lusin- and Sierpinski- sets, leading to a natural conjecture.

Date received: March 18, 2008