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On the extent of (discretely) star-Lindelof spaces.
by
Mikhail Matveev
Irvine, CA
A space X is star-Lindelof provided for every open cover U there is an at most countable subset A of X such that St(A, U)=X. If A can be chosen closed in X and discrete then X is said to be discretely star-Lindelof. It is clear that a T1 space of countable extent is discretely star-Lindelof. We show that a Tychonoff discretely star-Lindelof space may have arbitrarily big extent. On the other hand, the extent of a normal star-Lindelof space may not be greater than c.
Date received: June 27, 2000
Copyright © 2000 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 # caeu-51.