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Mat. Zametki, 1997, Volume 62, Issue 6, Pages 813–819 (Mi mz1670)  

This article is cited in 6 scientific papers (total in 6 papers)

Topology of the hyperspace of convex bodies of constant width

L. E. Bazilevich

Lviv Polytechnic National University

Abstract: The hyperspace of all convex bodies of constant width in Euclidean space $\mathbb R^n$, $n\ge2$, is proved to be homeomorphic to a contractible $Q$-manifold ($Q$ denotes the Hilbert cube). The proof makes use of an explicitly constructed retraction of the entire hyperspace of convex bodies on the hyperspace of convex bodies of constant width.

DOI: https://doi.org/10.4213/mzm1670

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English version:
Mathematical Notes, 1997, 62:6, 683–687

Bibliographic databases:

UDC: 515.12
Received: 14.04.1995

Citation: L. E. Bazilevich, “Topology of the hyperspace of convex bodies of constant width”, Mat. Zametki, 62:6 (1997), 813–819; Math. Notes, 62:6 (1997), 683–687

Citation in format AMSBIB
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\paper Topology of the hyperspace of convex bodies of constant width
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\yr 1997
\vol 62
\issue 6
\pages 813--819
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\jour Math. Notes
\yr 1997
\vol 62
\issue 6
\pages 683--687
\crossref{https://doi.org/10.1007/BF02355455}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Bazylevych, LE, “On convex bodies of constant width”, Topology and Its Applications, 153:11 (2006), 1699  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Dawson, RJM, “Cebysev Sets in Hyperspaces over R-n”, Canadian Journal of Mathematics-Journal Canadien de Mathematiques, 61:2 (2009), 299  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Zelinskii Yu., “Known Results and Open Problems in Hypercomplex Convexity”, Analele Stiint. Univ. Ovidius C., 22:1 (2014), 289–297  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Bazylevych L., Zarichnyi M., “Infinite-Dimensional Hyperspaces of Convex Bodies of Constant Width”, Topology Appl., 179:SI (2015), 215–220  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Antonyan S.A., Jonard-Perez N., Juarez-Ordonez S., “Hyperspaces of Convex Bodies of Constant Width”, Topology Appl., 196:B (2015), 347–361  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Belegradek I., “Hyperspaces of Smooth Convex Bodies Up to Congruence”, Adv. Math., 332 (2018), 176–198  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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