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.
