Small Valdivia compact spaces

Wieslaw Kubiś; Henryk Michalewski

doi:10.1016/j.topol.2005.09.010

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arXiv · math/0507062

Small Valdivia compact spaces

Wieslaw Kubiś·Henryk Michalewski

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Abstract

We prove a preservation theorem for the class of Valdivia compact spaces, which involves inverse sequences of ``simple'' retractions. Consequently, a compact space of weight $\loe\aleph_1$ 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 at most $\aleph_1$ 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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Wieslaw Kubiś, Henryk Michalewski. 2005-07-04. Small Valdivia compact spaces. https://doi.org/10.1016/j.topol.2005.09.010

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