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II Workshop on Coverings, Selections and Games in Topology
December 19-22, 2005
University of Lecce
Lecce, Italy

Organizers
(Organizing Committee) Cosimo Guido, Anna Frascella, Domenico Lenzi, Gabriella Zammillo. (Scientific Committee) Liljana Babinkostova, Cosimo Guido, Ljubisa Kocinac, Marion Scheepers, Boaz Tsaban

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On g-sets
by
Arnold W. Miller
University of Wisconsin, Madison

We will survey some recent results on g-sets and related properties. The notion of a g-set was invented by Gerlits and Nagy in 1982 in their study of the space of continuous functions C(X). It is also denoted S1(W, G) in the Scheepers terminology. An w-cover of X is a family of open sets U with the property that for every finite F Í X there exists U Î U with F Í U. X is a g set iff for every w-cover U there exists (Un Î U :n < w) such that every x Î X is in all but finitely many Un. The sequence (Un:n < w) is called a g-cover of X.

A related notion is that of a Borel-cover g-set, where we allow the relevant covers to be made up of Borel sets instead of open sets. Another notion is that of a relative g-set X Í Y where we are required to choose a g-cover of X from an w-cover of Y.

Date received: November 22, 2005

Copyright © 2005 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 # caqh-23.