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The 12th Summer Conference on General Topology and its Applications
August 12-16, 1997
Nipissing University
North Bay, ON, Canada

Organizers
Ted Chase, Boguslaw Schreyer, Jodi Sutherland, Murat Tuncali, Stephen Watson

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The combinatorics of Michael's problem
by
Justin Tatch Moore
University of Toronto

We will discuss some combinatorial principles related to the existence of a Michael space. Let P denote the space of irrationals and C denote the Cantor Set. Also \cov(M) will denote the minimum number of meager sets it takes to cover the Cantor set. If X is a non-Lindelöf space then let L(X) be the least cardinal \kappa for which there is an uncountable open cover of X of size \kappa with no countable subcover. The following theorems will be presented:

  1. The statement d = \cov(M) implies that there is a Michael space.

  2. If there is a Lindelöf space X (no assumptions on separation) whose product with P is not Lindelöf and cf(L(X ×P)) > \aleph0 then there is a subspace of (d+1) ×C which is a Michael space.

  3. If ZFC is consistent, then so is ZFC + "\cov(M) < b < d".

Date received: July 21, 1997

Copyright © 1997 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 Conferences Inc. Document # caap-11.