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International Conference on Topology and its Applications
August 23-27, 1999
Kanagawa University
Yokohama, Japan

Organizers
Yukinobu Yajima, the chairman, Masami Sakai, the vice-chairman, Yoshihiro Abe, Kazuhiro Sakai, Toshiji Terada, Kenichi Tamano, Akio Kato, Takao Hoshina, Hisao Kato, Kazuhiro Kawamura, Akira Koyama, Tsugunori Nogura

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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, does small diagonal imply G\delta-diagonal (for certain classes of spaces)? 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-diagonal; (3) there is in ZFC a locally compact space with a small diagonal but no G\delta-diagonal.

Date received: June 7, 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 # caby-10.