Starshapedness in convexity spaces

Krzysztof Kołodziejczyk

Compositio Mathematica (1985)

  • Volume: 56, Issue: 3, page 361-367
  • ISSN: 0010-437X

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Kołodziejczyk, Krzysztof. "Starshapedness in convexity spaces." Compositio Mathematica 56.3 (1985): 361-367. <http://eudml.org/doc/89746>.

@article{Kołodziejczyk1985,
author = {Kołodziejczyk, Krzysztof},
journal = {Compositio Mathematica},
keywords = {kernel of star-shaped sets; convex sets; convexity space; domain-finite space; join-hull commutative},
language = {eng},
number = {3},
pages = {361-367},
publisher = {Martinus Nijhoff Publishers},
title = {Starshapedness in convexity spaces},
url = {http://eudml.org/doc/89746},
volume = {56},
year = {1985},
}

TY - JOUR
AU - Kołodziejczyk, Krzysztof
TI - Starshapedness in convexity spaces
JO - Compositio Mathematica
PY - 1985
PB - Martinus Nijhoff Publishers
VL - 56
IS - 3
SP - 361
EP - 367
LA - eng
KW - kernel of star-shaped sets; convex sets; convexity space; domain-finite space; join-hull commutative
UR - http://eudml.org/doc/89746
ER -

References

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  1. [1] H. Brunn: Über Kemeigebiete. Math. Ann.73 (1913) 436-440. Zbl44.0560.01MR1511741JFM44.0560.01
  2. [2] V.W. Bryant and R.J. Webster: Convexity spaces. I. The basic properties. J. Math. Anal. Appl.37 (1972) 206-213. Zbl0197.48401MR296812
  3. [3] E. Degreef: Some results in generalized convexity. Doct. diss., Free University of Brussel (1981) 
  4. [4] P.C. Hammer: Extended topology: Domain finiteness. Indag. Math.25 (1963) 200-212. Zbl0118.17702MR175071
  5. [5] R.E. Jamison: A general theory of convexity. Doct. diss., University of Washington, Seattle (1974). 
  6. [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. Zbl0235.52001MR310766
  7. [7] K. Kołodziejczyk: On starshapedness of the union of closedsets in Rn. Colloq. Math. (to appear). Zbl0635.52006
  8. [8] K. Kołodziejczyk: The starshapedness number of a convexity space (preprint). Zbl0636.52002
  9. [9] M.A. Krasnosel'skii: Sur un critère pour qu'un domain soit étoilé. Mat. Sb.19 (1946) 309-310. Zbl0061.37705MR20248
  10. [10] F.W. Levi: On Helly's theorem and the axioms of convexity. J. Indian Math. Soc.15 (1951) 65-76. Zbl0044.19101MR43487
  11. [11] P. Mah, S.A. Naimpally and J.H.M. Whitfield: Linearization of a convexity space. J. London Math. Soc.13 (1976) 209-214. Zbl0326.52005MR415510
  12. [12] G. Sierksma: Axiomatic convexity theory and the convex product space. Doct. diss., University of Groningen (1976). Zbl0336.52001
  13. [13] V.P. Soltan: Starshaped sets in the axiomatic theory of convexity. Bull. Acad. Sci. Georgian SSR96 (1979) 45-48. Zbl0418.52003MR564757
  14. [14] F.A. Toranzos: Radial functions of convex and starshaped sets. Amer. Math. Monthly74 (1967) 278-280. Zbl0145.42802MR208469
  15. [15] F.A. Valentine: Convex Sets. New York: McGraw-Hill (1964). Zbl0129.37203MR170264

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