A compact group which is not Valdivia compact

Abstract

A compact space $K$ is {\em Valdivia compact} if it can be embedded in a Tikhonov cube $I^A$ in such a way that the intersection $K\cap \Sigma$ is dense in $K$, where $\Sigma$ is the sigma-product (= the set of points with countably many non-zero coordinates). We show that there exists a compact connected Abelian group of weight ${ø}_1$ which is not Valdivia compact, and deduce that Valdivia compact spaces are not preserved by open maps.

4 pages

References in corpus (1)

• Small Valdivia compact spaces

Cited by in corpus (11)

• Banach spaces with projectional skeletons
• Small Valdivia compact spaces
• Compact spaces generated by retractions
• Simultaneous projectional skeletons
• Subgroups of direct products closely approximated by direct sums
• Valdivia compact Abelian groups
• Spaces of continuous functions over Dugundji compacta
• Semi-Eberlein spaces
• Retractions of free MV-algebras and unital $\ell$-groups
• Weakly Corson compact trees
• Valdivia compact groups are products