A Construction of New Gul'ko and Talagrand Compacta
by
Petr Cízek

A compact space K is said to be Eberlein if it is homeomorphic to a weakly compact subset of a Banach space. A compact space K is said to be Talagrand (resp. Gul'ko) if the space of continuous functions with pointwise topology C_p(K) is K - analytic (resp. K - countably determined).

M. Talagrand has found an example of a Talagrand compact which is not Eberlein and of a Gul'ko compact which is not Talagrand.

Using the second example of Talagrand on more general metric spaces with certain descriptive properties, we will find a collection of such counter-examples.

Arbitrary co-analytic non-analytic set will give us an example of Gul'ko non-Talagrand compact, a Borel non-F_\sigma set will give us a Talagrand non-Eberlein compact, and finally a Borel non-F_\sigma\delta set will give us an example of a compact which is Talagrand but not a countable union of Eberlein compacta.

Date received: July 8, 1996

Copyright © 1996 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 # caaj-41.