Bulletin de la Société Royale des Sciences de Liège

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M. PIACQUADIO LOSADA, A. FORTE CUNTO & F. A. TORANZOS

MUST THE VISIBILITY FUNCTION OF AN OPEN SET BE CONTINUOUS?

(Volume 77 - Année 2008)
Article
Open Access

Abstract

The visibility function of a set S was defined in 1972 by G. Beer.  This function evaluates the Lebesgue outer measure of the star of each point of S.  The continuity of this function for compact sets was studied by its creator.  Recently, the present authors settled the problem of continuity in t he boundary of a compact set S.  The question of the continuity in the case where S is an open bounded set - proposed by G. Beer - is still unsettled.  We show here that the continuity of the visibility function does not depend on the boundedness of the open set S.

To cite this article

M. PIACQUADIO LOSADA, A. FORTE CUNTO & F. A. TORANZOS, «MUST THE VISIBILITY FUNCTION OF AN OPEN SET BE CONTINUOUS?», Bulletin de la Société Royale des Sciences de Liège [En ligne], Volume 77 - Année 2008, 1 - 8 URL : http://popups.ulg.be/0037-9565/index.php?id=590.

About:  M. PIACQUADIO LOSADA

DEPARTAMENTO DE MATEMÀTICA, FACULTAD DE CIENCIAS EXACTAS y NATURALES, UNIVERSIDAD DE BUENOS AIRES, gdutt@fibertel.corn.ar

About:  A. FORTE CUNTO

DEPARTAMENTO DE MATEMÀTICA, FACULTAD DE CIENCIAS EXACTAS y N ATURALES, UNIVERSIDAD DE BUENOS AIRES, aforte@dm.uba.ar

About:  F. A. TORANZOS

DEPARTAMENTO DE MATEMÀTICA, FACULTAD DE CIENCIAS EXACTAS y NATURALES, UNIVERSIDAD DE BUENOS AIRES