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arXiv · 0705.2867

Continuous selections and sigma-spaces

Dušan Repovš·Boaz Tsaban·Lyubomyr Zdomskyy
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Abstract

Assume that X is a metrizable separable space, and each clopen-valued lower semicontinuous multivalued map Phi from X to Q has a continuous selection. Our main result is that in this case, X is a sigma-space. We also derive a partial converse implication, and present a reformulation of the Scheepers Conjecture in the language of continuous selections.

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Dušan Repovš, Boaz Tsaban, Lyubomyr Zdomskyy. 2007-05-20. Continuous selections and sigma-spaces. https://doi.org/10.1016/j.topol.2008.03.025

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