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TIETZE - TYPE THEOREM FOR LOCALLY NONCONICAL CONVEX SETS
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.
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