Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T16:09:32.844Z Has data issue: false hasContentIssue false
  • English
  • Français

Continuous Families of Smooth Curves and Grünbaum’s Conjecture

Published online by Cambridge University Press:  20 November 2018

Tudor Zamfirescu  and
Andreana Zucco
Tudor Zamfirescu
Affiliation:
Universität Dortmund, Abteilung Mathematik, 46 Dortmund, Germany
Andreana Zucco
Affiliation:
Istituto di Geometria, Università di Torino, Via Principe Amedeo 8 10123 Torino, Italy
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

First we construct spreads consisting of analytic curves (circular arcs and segments), without points of finite multiplicity. Then we see that, in the sense of Baire categories, most such spreads have no points of finite multiplicity.

Keywords

52A37
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 3 , 01 September 1984 , pp. 345 - 350
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Zucco, A. Gandini, Sur une des conjectures de B. Grünbaum concernant les families continues de courbes, Rend Lincei, ser VIII, 68 (5), (1980), 416–419.Google Scholar
2. Grünbaum, B., Continuous families of curves, Can. J Math., 18 (1966) 529–537.Google Scholar
3. Grünbaum, B., Arrangements and Spreads, Lectures delivered at a regional conference on Combinatorial Geometry, University of Oklahoma (1971).Google Scholar
4. Jarniik, V., Über die Differenzierbarkeit stetiger Funktionen, Fund. Math., 21 (1933), 48–58.Google Scholar
5. Watson, K. S., Sylvester’s problem for spreads of curves, Can. J. Math. 32 (1980), 219–239.Google Scholar
6. Zamfirescu, T., On continuous families of curves. VI, Geom. Dedicata, 10 (1981), 205–217.Google Scholar