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Journal of Convex Analysis 11 (2004), No. 2, 267--284
Copyright Heldermann Verlag 2004

Pointedness, Connectedness, and Convergence Results in the Space of Closed Convex Cones

Alfredo Iusem
Inst. de Mathematica Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botanico, Rio de Janeiro, Brazil,

Alberto Seeger
University of Avignon, Dept. of Mathematics, 33 rue Louis Pasteur, 84000 Avignon, France,

Let K(H) denote the collection of all closed convex cones in a finite dimensional real Hilbert space H. Painleve-Kuratowski convergence in this space has been the subject of numerous publications. However, the link between convergence and pointedness has not been explored in its full extent. This note contributes to close this gap. Some results concerning the connected components of K(H) are also considered.

Keywords: pointed cone, solid cone, Painleve-Kuratowski convergence, polarity, connectedness.

MSC 2000: 52 A 07, 54 F 65.

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