Abstract
Combinatorial conditions of Krasnosel'skii-type involving concepts ofR-visibility and clearR-visibility are given to ensure that the dimension of theR-kernel of a proper subset ofR d is greater than or equal tok, 0<-k<d.
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Krasnosel'skii, M. A.: Sur un critère pour qu'un domaine soit étoilé. Mat. Sb.19 (61), 309–310 (1946) (in Russian, French summary).
Breen, M.: Krasnosel'skii-type theorems. Ann. New York Acad. Sci.440, 142–146 (1985).
Breen, M.: A characterization theorem for bounded starshaped sets in the plane. Proc. Amer. Math. Soc.94 693–698 (1985).
Breen, M.: Improved Krasnosel'skii theorems for the dimension of the kernel of a starshaped set. J. Geom.27, 175–179 (1986).
Cel, J.: Krasnosel'skii-type characterizations for a cone. Geom. Dedicata39, 139–153 (1991).
Cel, J.: Intersection formulae for the kernel of a cone. Geom. Dedicata39, 363–371 (1991).
Tietze, H.: Über Konvexheit im kleinen und im grossen und über gewisse den Punkten einer Menge zugeordnete Dimensionzahlen. Math. Z.28, 697–707 (1928).
Valentine, F. A.: Convex Sets. New York: McGraw-Hill. 1964.
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The author is with the Department of Mathematics of the University of Notre Dame Indiana, on leave from the Mathematical Institute of the Polish Academy of Sciences.
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Cel, J. Determining dimension of the kernel of a cone. Monatshefte für Mathematik 114, 83–88 (1992). https://doi.org/10.1007/BF01535573
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DOI: https://doi.org/10.1007/BF01535573