Continuous selections and \(\sigma \)-spaces (Q958510)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Continuous selections and \(\sigma \)-spaces |
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Continuous selections and \(\sigma \)-spaces (English)
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5 December 2008
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It is proved that \(X\) is a space in which \(F_\sigma\)-sets are simultaneously \(G_\delta\)-sets (a \(\sigma\)-space) if and only if each lower-semicontinuous multifunction defined on \(X\) and with values being closed-open subsets of a space homeomorphic to the space of rational numbers admits a continuous selection. Then connections with the Sheepers conjecture are explained and two open questions are posed.
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multifunction
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continuous selection
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\(b\)-scale
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lower-semicontinuity
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Fréchet filter
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Sheepers conjecture
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