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Conference in Honor of Alexander Arhangelskii
June 29 - July 3, 2003
Brooklyn College of the City University of New York
Brooklyn, NY, USA

Organizers
Raushan Buzyakova, Ralph Kopperman, Gerald Itzkowitz, Raymond Gittings, Susan Andima, Oleg Pavlov, Oleg Okunev, Dennis Burke, Vladimir Uspenskii, Witold Marciszewski, Stephen Watson, Hans-Peter Kunzi

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On D-property of function spaces and a class of spaces with Lindelof Cp
by
Raushan Buzyakova
Brooklyn College

A function \phi from X to the topology of X is called a neighbourhood assignment on X (in sense of Eric van Douwen) if x in \phi(x) for every x in X

A space X is called a D-space (in sense of Eric van Douwen) if for every neighbourhood assignment \phi on X there exists a closed discrete D subset X such that the union of \phi(d)'s covers X, where d in D.

A connection of D-property with classical theorems of Grothendieck and Baturov will be discussed.

It is shown that Cp over every compacta as well as over countably-compact spaces with certain restrictions are hereditarily D.

It is also shown that in general Cp over countably compact spaces does not have to be D. A counterexample is constructed. And a certain class of countably compact spaces with Lindelof Cp's will be discussed.

Date received: June 4, 2003

Copyright © 2003 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 Mathematical Conference Abstracts. Document # cajv-58.