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Keywords:
Corson compact space; Valdivia compact space; continuous image; ordinal segment
Corson compact space; Valdivia compact space; continuous image; ordinal segment
Summary:
We prove in particular that a continuous image of a Valdivia compact space is Corson provided it contains no homeomorphic copy of the ordinal segment $[0,\omega_1]$. This generalizes a result of R. Deville and G. Godefroy who proved it for Valdivia compact spaces. We give also a refinement of their result which yields a pointwise version of retractions on a Valdivia compact space.
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