Abstract
Assume that X ⊆ R {set minus} Q, and each clopen-valued lower semicontinuous multivalued map Φ : X ⇒ Q has a continuous selection φ{symbol} : X → Q. Our main result is that in this case, X is a σ-space. We also derive a partial converse implication, and present a reformulation of the Scheepers Conjecture in the language of continuous selections.
| Original language | English |
|---|---|
| Pages (from-to) | 104-109 |
| Number of pages | 6 |
| Journal | Topology and its Applications |
| Volume | 156 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Nov 2008 |
Bibliographical note
Funding Information:✩ The first and third authors were partially supported by the Slovenian Research Agency grants P1-0292-0101-04 and BI-UA/04-06-007. The second author was partially supported by the Koshland Center for Basic Research. * Corresponding author. E-mail addresses: [email protected] (D. Repovš), [email protected] (B. Tsaban), [email protected] (L. Zdomskyy). 1 Current address: Kurt Gödel Research Center for Mathematical Logic, Währinger Str. 25, A-1090 Vienna, Austria.
Funding
✩ The first and third authors were partially supported by the Slovenian Research Agency grants P1-0292-0101-04 and BI-UA/04-06-007. The second author was partially supported by the Koshland Center for Basic Research. * Corresponding author. E-mail addresses: [email protected] (D. Repovš), [email protected] (B. Tsaban), [email protected] (L. Zdomskyy). 1 Current address: Kurt Gödel Research Center for Mathematical Logic, Währinger Str. 25, A-1090 Vienna, Austria.
| Funders | Funder number |
|---|---|
| Koshland Center for Basic Research | |
| Javna Agencija za Raziskovalno Dejavnost RS | BI-UA/04-06-007, P1-0292-0101-04 |
Keywords
- Clopen-valued map
- Continuous selection
- Fréchet filter
- Lower semicontinuity
- Multivalued map
- b-Scale
- γ-Cover
- σ-Space