English

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.

Keywords

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}
}
R2 v1 2026-06-21T08:29:58.819Z