A compact convex set not convexly totally bounded

• Autorzy: Trombetta, G.
• Języki publikacji: EN

Abstrakty

EN

A simple example of a convex compact set contained in a quasi-Banach space which is not convexly totally bounded is given.

Słowa kluczowe

PL

przestrzeń Ribe'a; zbiór wypukły

EN

convex set; convexly totally bounded set; needle point; Ribe space

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2001
• Tom: Vol. 49, no 3
• Strony: 223--228
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Trombetta, G.

• Dipartimento di Matematica, Universita Della Calabria, 87036 Arcavata di Rende Cosenza), Italia

Bibliografia

• [1] E. de Pascale, G. Trombetta H. Weber, Convexly totally bounded and strongly totally bounded sets. Solution of a problem of Idzik, Ann. Sc. Norm. Super. Pisa. Cl. Sci., Serie IV, Vol. XX (3) (1993) 341-355.
• [2] A. Granas, KKM-maps and their applications to nonlinear problems, The Scotthis Book, ed.: R. D. Mauldin, Birkhäuser, Basel and Boston, Mass. 1981, 45-61.
• [3] A. Idzik, On -γ-almost fixed point theorem. The single valued case, Bull. Pol. Ac. Math., 35 (1987) 461-464.
• [4] A. Idzik, Almost fixed point theorems, Proc. Amer. Math. Soc., 104 (1988) 779-784.
• [5] N. J. Kalton, N. T. Peck, J. W. Roberts, An F-space sampler, London Math. Soc. Lecture Note Ser., 89 (1984).
• [6] N. T. Peck, L. Waelbroeck, Problem 58, Stud. Math., 38 (1970) 482.
• [7] M. Ribe, Examples for the nonlocally convex three space problem, Proc. Amer. Math. Soc., 237 (1979) 351-355.
• [8] J.3. W. Roberts, Pathological compact convex sets in the spaces P'([0,1]), p < 1, The Altgeld Book, University of Illinois, Functional Analysis Seminar, (1976).
• [9] S. Rolewicz, Metric linear spaces, PWN, Warszawa 1984.
• [10] H. Weher, Compact convex sets in nonlocally convex linear space, Note Mat., 12 (1992) 271-289.