|
Organizers |
Small Diagonals
by
Gary Gruenhage
Auburn University
According to M. Husek, a space X has a small diagonal if for every uncountable subset Y of X2\\Delta, there is an open set U containing \Delta such that Y\U is uncountable. Clearly a space with a G\delta-diagonal has a small diagonal; the question is, when does small diagonal imply G\delta-diagonal? This question for compact T2-spaces is a well-known and still not completely solved problem of Husek, though Juhasz has shown that CH implies a positive answer. Here we show: (1) the answer for countably compact spaces depends on your set theory; (2) there are consistent examples of regular hereditarily Lindelöf, and consistent with CH examples of regular Lindelöf, spaces with a small diagonal but no G\delta-diagonal; (3) there is in ZFC a locally compact space with a small diagonal but no G\delta diagonal.
Date received: February 10, 1999
Copyright © 1999 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 # caca-32.