Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T15:26:29.165Z Has data issue: false hasContentIssue false
  • English
  • Français

Typical Convex Sets of Convex Sets

Part of: General convexity

Published online by Cambridge University Press:  09 April 2009

T. Schwarz  and
T. Zamfirescu
T. Schwarz
Affiliation:
Department of MathematicsOhio State UniversityMansfield, Ohio 44906, U.S.A.
T. Zamfirescu
Affiliation:
Fachbereich MathematikUniversität Dortmund46 Dortmund, Federal Republic of Germany
Rights & Permissions [Opens in a new window]

Extract

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.

There exists a natural notion of convexity in the space of all compact convex sets in D. Thus, we may consider the space of all bounded closed convex families of compact convex sets. We present here a strange generic extremal behaviour of the elements of this space.

MSC classification

Secondary: 52A05: Convex sets without dimension restrictions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 3 , December 1987 , pp. 287 - 290
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Klee, V., ‘Some new results on smoothness and rotundity in normed linear spaces,’ Math. Ann. 139 (1959), 51–63.CrossRefGoogle Scholar
[2]Kuratowski, C., Topologie I (Warszawa, 1958).Google Scholar
[3]Zamfirescu, T., ‘Many endpoints and few interior points of geodesies‘, Invent. Math. 69 (1982), 253–257.CrossRefGoogle Scholar
[4]Zamfirescu, T., ‘Using Baire categories in geometry,’ Rend. Sent. Mat. Univ. Politec. Torino 43 (1985), 67–88.Google Scholar