Bulletin de la Société Royale des Sciences de Liège Bulletin de la Société Royale des Sciences de Liège -  Volume 69 - Année 2000  Numéro 1 

TIETZE-TYPE THEOREM FOR PARTIALLY CONVEX PLANAR SETS

J. Cel, 

Warszawska 24c/20, 26-200 Końskie, Poland

Abstract

Let S be a nonempty subset of R2 and   R2 a set of directions.  S is called V-convex or partially convex relative to  at a point s  clS if and only if there exists a neighbourhood N of s in R2 such that the intersection of any straight line parallel to a vector in  with S  N is connected or empty S is called -convex or partially convex relative to  if and only if the intersection of any straight line parallel to a vector in  with S is connected or empty.  It is proved that if  is open, S is connected and open or polygonally connected and closed, and -convex at every boundary point, then it is -convex.  This contributes to a recent work of Rawlins, Wood, Metelskij and others.

Pour citer cet article

J. Cel, «TIETZE-TYPE THEOREM FOR PARTIALLY CONVEX PLANAR SETS», Bulletin de la Société Royale des Sciences de Liège [En ligne], Volume 69 - Année 2000, Numéro 1, 17 - 20 URL : http://popups.ulg.be/0037-9565/index.php?id=1660.