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Embedding of the ordinal segment \([0, \omega _1]\) into continuous images of Valdivia compacta. (English) Zbl 1009.54017

The main result: A continuous image of a Valdivia compact space is Corson if and only if it contains no homeomorphic copy of the ordinal segment \([0,\omega _1]\), and there are another two equivalent conditions. This generalizes a result of R. Deville and G. Godefroy [Proc. Lond. Math. Soc., III. Ser. 67, No. 1, 183-199 (1993; Zbl 0798.46008)] who proved it for Valdivia compact spaces. The paper also contains a refinement of their result which yields a pointwise version of retractions on Valdivia compact spaces.

MSC:

54C05 Continuous maps
54D30 Compactness

Citations:

Zbl 0798.46008
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