Covering properties of sets of reals - the Hurewicz conjecture
by
Arnold Miller
University of Wisconsin

We will discuss various covering properties of sets of reals which are due to Rothberger, Menger, Hurewicz, Gerlits-Nagy, and Borel. In particular, we will discuss a conjecture of Hurewicz which is analogous to the Borel conjecture about strong measure zero sets of reals. A set of reals X has the Hurewicz property, if whenever we are give a sequence <U_n: n in \omega> of open covers of X we can choose <V_n in [U]^\omega : n in \omega> such that every element of X is in all but finitely many \cup V_n. It easy to see that if X is \sigma-compact (the countable union of compact sets), then X has the Hurewicz property. The Hurewicz conjecture is that the converse is true.

Date received: February 14, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # caab-84.