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Continuous images and other topological properties of Valdivia compacta. (English) Zbl 0989.54019

The author gives an alternative definition of Valdivia compactness in terms of a newly defined concept of \(\Sigma\)-subsets. The properties of such subsets are studied and \(\Sigma\)-subsets are also used to define Corson compact space. The main result, to interrelate Valdivia compactness and Corson compactness is as follows:
For a compact Hausdorff space \(K\) the following assertions are equivalent:
(i) Every continuous image of \(K\) is a Valdivia compactum,
(ii) Every at most two-to-one continuous image of \(K\) is a Valdivia compactum,
(iii) \(K\) is a Corson compactum.

MSC:

54C05 Continuous maps
54D30 Compactness
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