On some questions of A.V. Arhangel'skii
by
Gary Gruenhage
Auburn University

One of the great strengths of Shura's leadership in general topology has been his ability to come up with good questions. It is remarkable, considering the amazing number and variety of his questions, that almost none have been trivial. Some have become major long-standing problems in the field, but even the ones that have been answered fairly quickly have generally required some new insight into the concepts involved, and thus have helped move our field forward.

In this talk I will present solutions to some of his recent questions, primarily on the topic of D-spaces. In particular, we show that every Corson compact space is hereditarily a D-space, and that countably compact spaces which are finite unions of D-spaces must be compact.

Date received: May 27, 2003