Starshapedness in convexity spaces
Kołodziejczyk, Krzysztof
Compositio Mathematica, Tome 56 (1985), p. 361-367 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1985-01-01
@article{CM_1985__56_3_361_0,
     author = {Ko\l odziejczyk, Krzysztof},
     title = {Starshapedness in convexity spaces},
     journal = {Compositio Mathematica},
     volume = {56},
     year = {1985},
     pages = {361-367},
     zbl = {0584.52001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1985__56_3_361_0}
}

Kołodziejczyk, Krzysztof. Starshapedness in convexity spaces. Compositio Mathematica, Tome 56 (1985) pp. 361-367. http://gdmltest.u-ga.fr/item/CM_1985__56_3_361_0/

[1] H. Brunn: Über Kemeigebiete. Math. Ann. 73 (1913) 436-440. | JFM 44.0560.01 | MR 1511741

[2] V.W. Bryant and R.J. Webster: Convexity spaces. I. The basic properties. J. Math. Anal. Appl. 37 (1972) 206-213. | MR 296812 | Zbl 0197.48401

[3] E. Degreef: Some results in generalized convexity. Doct. diss., Free University of Brussel (1981)

[4] P.C. Hammer: Extended topology: Domain finiteness. Indag. Math. 25 (1963) 200-212. | MR 175071 | Zbl 0118.17702

[5] R.E. Jamison: A general theory of convexity. Doct. diss., University of Washington, Seattle (1974). | MR 2624693

[6] D.C. Kay and E.W. Womble: Axiomatic convexity theory and relationships between the Carathéodory, Helly and Radon numbers. Pacific J. Math. 38 (1971) 471-485. | MR 310766 | Zbl 0235.52001

[7] K. Kołodziejczyk: On starshapedness of the union of closedsets in Rn. Colloq. Math. (to appear). | Zbl 0635.52006

[8] K. Kołodziejczyk: The starshapedness number of a convexity space (preprint).

[9] M.A. Krasnosel'Skii: Sur un critère pour qu'un domain soit étoilé. Mat. Sb. 19 (1946) 309-310. | MR 20248 | Zbl 0061.37705

[10] F.W. Levi: On Helly's theorem and the axioms of convexity. J. Indian Math. Soc. 15 (1951) 65-76. | MR 43487 | Zbl 0044.19101

[11] P. Mah, S.A. Naimpally and J.H.M. Whitfield: Linearization of a convexity space. J. London Math. Soc. 13 (1976) 209-214. | MR 415510 | Zbl 0326.52005

[12] G. Sierksma: Axiomatic convexity theory and the convex product space. Doct. diss., University of Groningen (1976). | Zbl 0336.52001

[13] V.P. Soltan: Starshaped sets in the axiomatic theory of convexity. Bull. Acad. Sci. Georgian SSR 96 (1979) 45-48. | MR 564757 | Zbl 0418.52003

[14] F.A. Toranzos: Radial functions of convex and starshaped sets. Amer. Math. Monthly 74 (1967) 278-280. | MR 208469 | Zbl 0145.42802

[15] F.A. Valentine: Convex Sets. New York: McGraw-Hill (1964). | MR 170264 | Zbl 0129.37203