Oscillation Revisited
In previous joint work by G. Beer and S. Levi, the authors studied the oscillation Ω( f , A ) of a function f between metric spaces 〈 X , d 〉 and 〈 Y , ρ 〉 at a nonempty subset A of X , defined so that when A = { x }, we get Ω( f ,{ x }) = ω ( f , x ), where ω ( f , x ) denotes the classical notion...
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| Veröffentlicht in: | Set-valued and variational analysis 2017-09, Vol.25 (3), p.603-616 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In previous joint work by G. Beer and S. Levi, the authors studied the oscillation Ω(
f
,
A
) of a function
f
between metric spaces 〈
X
,
d
〉 and 〈
Y
,
ρ
〉 at a nonempty subset
A
of
X
, defined so that when
A
= {
x
}, we get Ω(
f
,{
x
}) =
ω
(
f
,
x
), where
ω
(
f
,
x
) denotes the classical notion of oscillation of
f
at the point
x
∈
X
. The main purpose of this article is to formulate a general joint continuity result for (
f
,
A
)↦Ω(
f
,
A
) valid for continuous functions. |
|---|---|
| ISSN: | 1877-0533 1877-0541 |
| DOI: | 10.1007/s11228-017-0425-8 |