Axiomatic convexity theory and relationships between the Carathéodory, Helly, and Radon numbers.
David C. Kay and Eugene W. Womble
Source: Pacific J. Math. Volume 38, Number 2
(1971), 471-485.
First Page:
Show
Hide
Primary Subjects:
52A35
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.pjm/1102970059
Zentralblatt MATH identifier: 0235.52001
Mathematical Reviews number (MathSciNet): MR0310766
References
[1] L. Danzer, B. Grunbaum, V. Klee, Hetty's theorem and its relatives, Amer. Math. Soc, Proceedings of Symposia in Pure Mathematics, 7 (1963), 101-180.
Mathematical Reviews (MathSciNet): MR28:524
Zentralblatt MATH: 0132.17401
[2] A. Dvoretzky, A converse of Hetty's theorem on convex sets, Pacific J. Math., 5 (1955), 345-350.
Mathematical Reviews (MathSciNet): MR17:294b
Zentralblatt MATH: 0065.15301
[3] J. Eckhoff, Der Satz von Radon in konvexen ProduktstrukturenI, Monatshefte fur Mathematik, 72 (1968), 303-314.
Mathematical Reviews (MathSciNet): MR38:1607
Zentralblatt MATH: 0159.51701
[4] J. W. Ellis, A general set-separation theorem, Duke Math. J., 19 (1952), 417-421.
Mathematical Reviews (MathSciNet): MR14:146i
Zentralblatt MATH: 0047.28601
[5] P. C. Hammer, Kuratowski'sclosure theorem, Nieuw Archief voor Wiskunde, 8 (1960), 74-80.
Mathematical Reviews (MathSciNet): MR26:6922
Zentralblatt MATH: 0137.15503
[6] P. C. Hammer,Extended topology: Caratheodory's theorem on convex hulls, Rendiconti del Circulo Mathematico de Palermo, 14 (1965), 34-42. 7.1Semispaces and the topology of convexity, Amer. Math. Soc, Proceedings of Symposia in Pure Mathematics, 7 (1963), 305-316.
Mathematical Reviews (MathSciNet): MR35:2255
Zentralblatt MATH: 0151.29304
[8] W. Koenen, The Kuratowskiclosure problem in the topology of convexity, Amer. Math. Monthly, 73 (1966), 704-708.
Mathematical Reviews (MathSciNet): MR34:6746
Zentralblatt MATH: 0144.44501
[9] F. W. Levi, On Hetty's theorem and the axioms of convexity, J. Indian Math. Soc, 15 (1951), 65-76.
Mathematical Reviews (MathSciNet): MR13:271a
Zentralblatt MATH: 0044.19101
[10] J. R. Reay, Caratheodory theorems in convex product structures, Pacific J. Math., 35 (1970), 227-230.
Mathematical Reviews (MathSciNet): MR42:8395
Zentralblatt MATH: 0182.55601
Pacific Journal of Mathematics
