Small Valdivia compact spaces |
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Authors: | Wies?aw Kubi? Henryk Michalewski |
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Affiliation: | a Akademia ?wi?tokrzyska, Kielce, Poland b Warsaw University, Warsaw, Poland |
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Abstract: | We prove a preservation theorem for the class of Valdivia compact spaces, which involves inverse sequences of retractions of a certain kind. Consequently, a compact space of weight?ℵ1 is Valdivia compact iff it is the limit of an inverse sequence of metric compacta whose bonding maps are retractions. As a corollary, we show that the class of Valdivia compacta of weight?ℵ1 is preserved both under retractions and under open 0-dimensional images. Finally, we characterize the class of all Valdivia compacta in the language of category theory, which implies that this class is preserved under all continuous weight preserving functors. |
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Keywords: | primary, 54D30 secondary, 54C15, 54B35 |
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