On the Choquet–Dolecki Theorem

In this paper, we prove that if a multifunction Φ: T → Xfrom a first countable space Tinto a space Xwith property ( ∗ ) is upper semicontinuous at a point t 0 ∈ T, then the active boundary of Φ at t 0is compact. Moreover, we also show that if Xis an angelic space, then the active boundary of Φ at t...

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Veröffentlicht in:	Journal of mathematical analysis and applications 1999-06, Vol.234 (1), p.1-5
Hauptverfasser:	Cao, Jiling, Moors, Warren, Reilly, Ivan
Format:	Artikel
Sprache:	eng
Schlagworte:	angelic Dieudonné complete Exact sciences and technology Functional analysis kernel Mathematical analysis Mathematics multifunction Sciences and techniques of general use
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	In this paper, we prove that if a multifunction Φ: T → Xfrom a first countable space Tinto a space Xwith property ( ∗ ) is upper semicontinuous at a point t 0 ∈ T, then the active boundary of Φ at t 0is compact. Moreover, we also show that if Xis an angelic space, then the active boundary of Φ at t 0is the smallest kernel of Φ at t 0.
ISSN:	0022-247X 1096-0813
DOI:	10.1006/jmaa.1998.6239