Continuous selections and sigma-spaces
General Topology
2011-08-08 v3 Logic
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.
Cite
@article{arxiv.0705.2867,
title = {Continuous selections and sigma-spaces},
author = {Dušan Repovš and Boaz Tsaban and Lyubomyr Zdomskyy},
journal= {arXiv preprint arXiv:0705.2867},
year = {2011}
}