Continuity of multifunctions characterized by Steiner selections

D. Dentcheva

doi:10.1016/S0362-546X(01)00327-3

Continuity of multifunctions characterized by Steiner selections

D. Dentcheva

Research output: Contribution to journal › Conference article › peer-review

4 Scopus citations

Abstract

We consider set-valued mappings defined on a topological space with closed convex images Rⁿ. The measurability of a multifunction is characterized by the existence of a Castaing representation for it: a countable set of measurable selections that pointwise fills up the graph of the multifunction. Our aim is to construct a Castaing representation that characterizes Hausdorff continuity of the multifunction. The construction uses generalized Steiner points.

Original language	English
Pages (from-to)	1985-1996
Number of pages	12
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	47
Issue number	3
DOIs	https://doi.org/10.1016/S0362-546X(01)00327-3
State	Published - Aug 2001
Event	3rd World Congress of Nonlinear Analysts - Catania, Sicily, Italy Duration: 19 Jul 2000 → 26 Jul 2000

Keywords

Castaing representation
Continuity and measurability of multifunctions
Selections
Steiner center

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10.1016/S0362-546X(01)00327-3

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title = "Continuity of multifunctions characterized by Steiner selections",

abstract = "We consider set-valued mappings defined on a topological space with closed convex images Rn. The measurability of a multifunction is characterized by the existence of a Castaing representation for it: a countable set of measurable selections that pointwise fills up the graph of the multifunction. Our aim is to construct a Castaing representation that characterizes Hausdorff continuity of the multifunction. The construction uses generalized Steiner points.",

keywords = "Castaing representation, Continuity and measurability of multifunctions, Selections, Steiner center",

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N2 - We consider set-valued mappings defined on a topological space with closed convex images Rn. The measurability of a multifunction is characterized by the existence of a Castaing representation for it: a countable set of measurable selections that pointwise fills up the graph of the multifunction. Our aim is to construct a Castaing representation that characterizes Hausdorff continuity of the multifunction. The construction uses generalized Steiner points.

AB - We consider set-valued mappings defined on a topological space with closed convex images Rn. The measurability of a multifunction is characterized by the existence of a Castaing representation for it: a countable set of measurable selections that pointwise fills up the graph of the multifunction. Our aim is to construct a Castaing representation that characterizes Hausdorff continuity of the multifunction. The construction uses generalized Steiner points.

KW - Castaing representation

KW - Continuity and measurability of multifunctions

KW - Selections

KW - Steiner center

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U2 - 10.1016/S0362-546X(01)00327-3

DO - 10.1016/S0362-546X(01)00327-3

M3 - Conference article

AN - SCOPUS:0035425449

SN - 0362-546X

VL - 47

SP - 1985

EP - 1996

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 3

T2 - 3rd World Congress of Nonlinear Analysts

Y2 - 19 July 2000 through 26 July 2000

ER -

Continuity of multifunctions characterized by Steiner selections

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Keywords

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