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 LOCALLY NONCONICAL CONVEX SETS

J. Cel, 

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

Abstract

A convex subset Q of a real topological linear space L is called locally nonconical at a point q  Q if and only if there exists a relative neighbourhood Qq of q in Q such that for every two points x, y  Qq there is a relative neighbourhood Q, of x in Q such that Qx + (y - x)  Q.  Q is called locally nonconical if and only if this condition is satisfied for every two points x, y  Q.  It is proved that Q is locally nonconical if and only if it is locally nonconical at every boundary point belonging to Q.  This contributes to a recent work of Shell.

To cite this article

J. Cel, «TIETZE - TYPE THEOREM FOR LOCALLY NONCONICAL CONVEX SETS», Bulletin de la Société Royale des Sciences de Liège [En ligne], Volume 69 - Année 2000, Numéro 1, 13 - 15 URL : http://popups.ulg.be/0037-9565/index.php?id=1655.