Journal of Mathematical Sciences

, Volume 79, Issue 6, pp 1381–1383 | Cite as

On the topology of the Steiner symmetrization mapping

  • L. E. Bazilevich
Article
  • 24 Downloads

Abstract

We prove that the Steiner symmetrization mapping on the hyperspace of convex bodies in ℝ2 is soft and homeomorphic to a fibration in the bundle of Q-manifolds over any compact subset in the hyperspace of symmetric nonpolyhedral subsets.

Keywords

Compact Subset Convex Body Symmetrization Mapping Steiner Symmetrization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    K. Leichtweiss,Konvexe Menge, Springer, Berlin (1980).Google Scholar
  2. 2.
    T. A. Chapman,Lectures on Hilbert Cube Manifolds, American Mathematical Society, Providence (1976).Google Scholar
  3. 3.
    E. V. Shchepin, “Functors and uncountable degrees of compact sets,”Usp. Mat. Nauk,36, No. 3, 3–62 (1981).MATHMathSciNetGoogle Scholar
  4. 4.
    H. Torunczyk and J. West, “Fibrations and bundles with Hilbert cube manifold fibers,”Mem. Amer. Math. Soc., No. 406 (1989).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • L. E. Bazilevich

There are no affiliations available

Personalised recommendations