×
Wegner, Gerd

d-collapsing and nerves of families of convex sets. (English) Zbl 0308.52005

Arch. Math. 26, 317-321 (1975).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0308.52005

Cited in 5 Reviews
Cited in 51 Documents

MSC:

52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
55U05 Abstract complexes in algebraic topology
Cite Review PDF
Full Text: DOI

References:

[1] E. Helly, Über Mengen konvexer Körper mit gemeinschaftlichen Punkten. J.-Ber. Deutsch. Math.-Verein.32, 175-176 (1923). · JFM 49.0534.02
[2] E. Helly, Über Systeme abgeschlossener Mengen mit gemeinschaftlichen Punkten. Monatsh. Math.37, 281-302 (1930). · JFM 56.0499.03 · doi:10.1007/BF01696777
[3] J. H. C. Whitehead, Simplicial spaces, nuclei andm-groups. Proc. London Math. Soc.45, 243-327 (1939). · Zbl 0022.40702 · doi:10.1112/plms/s2-45.1.243
[4] J. Leray, Sur la forme des espaces topologiques et sur les points fixes des representations. J. Math. Pures Appl.24, 95-167 (1945). · Zbl 0060.40703
[5] C. G. Lekkerkerker andJ. C. Boland, Representation of a finite graph by a set of intervals on the real line. Fund. Math.51, 45-64 (1962). · Zbl 0105.17501
[6] L. Danzer, B. Grünbaum andV. Klee, Helly’s theorem and its relatives. In: Proc. Sympos. pure Math.7, Convexity, 101-180 (1963).
[7] E. C. Zeeman, On the dunce hat. Topology2, 341-358 (1964). · Zbl 0116.40801 · doi:10.1016/0040-9383(63)90014-4
[8] G.Wegner, Eigenschaften der Nerven homologisch-einfacher Familien im Rn. Diss. Göttingen 1967.
[9] B.Grünbaum, Incidence patterns of graphs and complexes. In: The Many Facets of Graph Theory, Proc. Conf. Western Michigan Univ. 1968, pp. 115-128 (1969).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.