Abstract
To study intersections of embedded bounded closed sets in Banach space, a numerical parameter was introduced earlier; in a certain sense, this parameter describes the deviation of the shape of a set from that of a sphere. Critical values of this parameter for some classes of Banach spaces are determined, a new numerical parameter serving the same purpose is introduced, and the relation between the two parameters is examined.
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N. N. Vakhaniya and I. I. Kartsivadze, “A remark on the intersection of a sequences of embedded closed sets”Mat. Zametki [Math. Notes],3, No. 2, 165–170 (1968).
G. Z. Chelidze, “On intersections of sequences of embedded closed sets in Banach spaces,”Mat. Zametki [Math. Notes],63, No. 2, 310–312 (1998).
G. Chelidze, “A counter example in a theorem of the intersection of embedded closed sets,”Bull. Acad. Sci. Georgia,156, No. 2, 207–209 (1997).
G. Chelidze,Bull. Acad. Sci. Georgia,159, 5–6 (1999).
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Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 303–310, August, 2000.
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Chelidze, G.Z. On critical values of numerical parameters characterizing intersections of embedded sets. Math Notes 68, 263–269 (2000). https://doi.org/10.1007/BF02675352
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DOI: https://doi.org/10.1007/BF02675352