Revistes Catalanes amb Accés Obert (RACO)

A characterization of Valdivia compact spaces

Ondřej Kalenda

Resum


We characterize Valdivia compact spaces $K$ in terms of $\mathcal{C}(K)$ endowed with a topology introduced by M. Valdivia (1991). This generalizes R. Pol’s characterization of Corson compact spaces. Further we study duality, products and open continuous images of Valdivia compact spaces. We prove in particular that the dual unit ball of $\mathcal{C}(K)$ is Valdivia whenever $K$ is Valdivia and that the converse holds whenever $K$ has a dense set of $G_\delta$ points. Another result is that any open continuous image of a Valdivia compact space with a dense set of $G_\delta$ points is again Valdivia.

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