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J. Cel

TIETZE - TYPE THEOREM FOR LOCALLY NONCONICAL CONVEX SETS

Article Open Access
: locally nonconical convex set, Tietze-type theorem

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.

Pour citer cet 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.ac.be/0037-9565/index.php?id=1655.

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