Good, splendid, and Jakovlev
by
Istvan Juhasz
A. Renyi Institute of Mathematics

A regular space is called good if it is both countably compact and locally countable. It is splendid if, in addition, all countable subsets have countable closures. First we survey what is known about the possible sizes of good and splendid spaces, respectively. Then we define Jakovlev spaces that are closely related to good spaces and are of independent interest because of their connection to some very old problems of Arhangelskii concerning weakly first countable compacta. Some recent joint results with Abraham and Gorelic will be presented about the possible sizes of Jakovlev spaces.

Date received: March 16, 2006