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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, iusp@impa.br
Alberto Seeger
University of Avignon, Dept. of Mathematics, 33 rue Louis Pasteur, 84000 Avignon, France,
alberto.seeger@univ-avignon.fr
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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