On a certain class of Valdivia compact spaces
by
Arkady Leiderman
Ben-Gurion University of the Negev, Beer-Sheva, Israel
Coauthors: Wieslaw Kubis (Katowice, Poland)

A compact Hausdorff space K is called a Valdivia compact space if there is a homeomorphic embedding h from K to some product of reals R^T such that the intersection of h(K) with Sigma-product is dense in h(K). A comprehensive survey is the work by O. Kalenda [1].

We call K a semi-Eberlein compact space if K admits a better embedding: such that the intersection of h(K) with c₀(T) is dense in h(K). Each adequate compact is semi-Eberlein. The segment of countable ordinals including \omega₁ provides an example of a Valdivia compact which is not semi-Eberlein. We want to investigate the properties of semi-Eberlein compact spaces. Are they essentially better like Eberlein compact spaces in comparison with Corson compact spaces?

In my talk I'll present some preliminary results and formulate open problems.

References:

[1] O.Kalenda "Valdivia compact spaces in topology and Banach space theory", Extracta Math. 15(2000), N 1, 1-85.

Date received: June 3, 2003