Convexity ranks in higher dimensions

Fundamenta Mathematicae

Volumn 164, Issue 2, 2000, Pages 143-163

  Kojman, Menachem ^a  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Cantor Bendixson degree; Continuum hypothesis; Convexity; Convexity number; Polish vector space

Indexed keywords

EID: 0001012579     PISSN: 00162736     EISSN: None     Source Type: Journal    
DOI: 10.4064/fm-164-2-143-163     Document Type: Article

References (20)

1. M. Breen, A decomposition theorem for m-convex sets, Israel J. Math. 24 (1976), 211-216.
2. d analogue of Valentine's theorem on 3-convex sets, ibid., 206-210.
3. M. Breen and D. C. Kay, General decomposition theorems for m-convex sets in the plane, ibid., 217-233.
4. G. Cantor, Ueber unendliche, lineare Punktmannichfaltigkeiten, Nr. 6, Math. Ann. 23 (1884), 453-488.
5. M. M. Day, Strict convexity and smoothness, Trans. Amer. Math. Soc. 78 (1955), 516-528.
6. H. G. Eggleston, A condition for a compact plane set to be a union of finitely many convex sets, Proc. Cambridge Philos. Soc. 76 (1974), 61-66.
7. δ sets, in preparation.
8. m, Israel J. Math. 8 (1970), 39-52.
9. A. S. Kechris and A. Louveau, Descriptive Set Theory and the Structure of Sets of Uniqueness, London Math. Soc. Lecture Note Ser. 128, Cambridge Univ. Press, 1987.
10. A. S. Kechris, A. Louveau and W. H. Woodin, The structure of σ-ideals of compact sets, Trans. Amer. Math. Soc. 301 (1987), 263-288.
11. V. Klee, Dispersed Chebyshev sets and covering by balls, Math. Ann. 257 (1981), 251-260.
12. 2, Israel J. Math., in press.
13. M. Kojman, M. A. Perles and S. Shelah, Sets in a Euclidean space which are not a countable union of convex subsets, Israel J. Math. 70 (1990), 313-342.
14. J. F. Lawrence, W. R. Hare, Jr. and J. W. Kenelly, Finite unions of convex sets, Proc. Amer. Math. Soc. 34 (1972), 225-228.
15. 1 spaces and their representing matrices, Acta Math. 126 (1971), 165-194.
16. J. Lindenstrauss and R. R. Phelps, Extreme point properties of convex bodies in reflexive Banach spaces, Israel J. Math. 6 (1968), 39-48.
17. J. Matoušek and P. Valtr, On visibility and covering by convex sets, ibid. 113 (1999), 341-379.
18. A. A. Milyutin, Ismorphisms of the spaces of continuous functions over compact sets of cardinality of the continuum, Teor. Funktsiǐ Funktsional. Anal. i Prilozhen. 2 (1966), 150-156.
19. 6 convex sets, Israel J. Math. 70 (1990), 305-312.
20. F. A. Valentine, A three point convexity property, Pacific J. Math. 7 (1957), 1227-1235.