On order and metric convexities in Z n
Changat, M. ; Vijayakumar, A.
Compositio Mathematica, Tome 84 (1992), p. 57-65 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1992-01-01
@article{CM_1992__82_1_57_0,
     author = {Changat, M. and Vijayakumar, A.},
     title = {On order and metric convexities in $Z^n$},
     journal = {Compositio Mathematica},
     volume = {84},
     year = {1992},
     pages = {57-65},
     mrnumber = {1154161},
     zbl = {0758.52010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1992__82_1_57_0}
}

Changat, M.; Vijayakumar, A. On order and metric convexities in $Z^n$. Compositio Mathematica, Tome 84 (1992) pp. 57-65. http://gdmltest.u-ga.fr/item/CM_1992__82_1_57_0/

[1] L. Danzer, B. Grunbaum and V. Klee, Helly's theorem and its relatives, Amer. Math. Soc. Proc. of Symposia in Pure Mathematics 7 (1963) 101-180. | MR 157289 | Zbl 0132.17401

[2] J.P. Doignon, Convexity in Crystallographical lattices, J. Geometry 3 (1973), 71-85. | MR 387090 | Zbl 0245.52004

[3] S.P. Franklin, Some results on order convexity, Amer. Math. Monthly 69 (1962) 357-359. | MR 1531672 | Zbl 0106.24401

[4] R.E. Jamison, Partition numbers for trees and ordered sets, Pacific J. Math., 96 (1981) 115-140. | MR 634767 | Zbl 0482.52010

[5] M. Lassak, The Helly dimension for Cartesian products of metric spaces, Mat. Issled, 10(2) (1975) 159-167. | MR 397566 | Zbl 0338.54020

[6] F.W. Levi, On Helly theorem and the axioms of convexity, J. Indian Math. Soc., 15 Part A (1951) 65-76. | MR 43487 | Zbl 0044.19101

[7] E. Sampathkumar, Convex sets in a graph, Ind. J. Pure. Appl. Maths., 15(10) (1984), 1065-1071. | MR 765010 | Zbl 0563.52001

[8] G. Sierksma, Caratheodory and Helly numbers of convex product structures, Pacific J. Math. 61 (1975), 275-282. | MR 397562 | Zbl 0301.52002

[9] V.P. Soltan, Some questions in the abstract theory of convexity, Soviet Math. Dokl., 17(3) (1976), 730-733. | Zbl 0348.52002

[10] V.P. Soltan, d-convexity in finite metric spaces, Bull. Akad. Stince RSS, Moldoven No. 2, 94 (1978), 29-33. | MR 509511 | Zbl 0394.52001

[11] A. Vijayakumar, Some characterization theorems for the discrete holometric space, Collect. Math. 38 (1987), 123-129. | MR 988950 | Zbl 0668.51011