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Mat. Zametki, 2008, Volume 84, Issue 5, Pages 658–666 (Mi mz4094)  

This article is cited in 1 scientific paper (total in 1 paper)

Hyperspace of Max-Plus Convex Compact Sets

L. E. Bazilevich

Lviv Polytechnic National University

Abstract: The hyperspace $\operatorname{mpcc}(\mathbb R^n)$ of max-plus convex compact subsets of $\mathbb R^n$, $n\ge2$, is considered. The main result is as follows: this hyperspace is a contractible manifold modeled on the Hilbert cube $Q$. It is also shown that the projection mapping $\operatorname{mpcc}(\mathbb R^n) \to\operatorname{mpcc}(\mathbb R^m)$, $n\ge m$, is open. Moreover, it is proved that the hyperspace $\operatorname{mpcc}(I^{\omega_1})$ of the Tikhonov [Tychonoff] cube $I^{\omega_1}$ is homeomorphic to $I^{\omega_1}$.

Keywords: compact convex set, max-plus convexity, contractible manifold, topological linear space, Hilbert cube, Tikhonov cube, retract, separable metric space

DOI: https://doi.org/10.4213/mzm4094

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English version:
Mathematical Notes, 2008, 84:5, 615–622

Bibliographic databases:

UDC: 515.12
Received: 23.04.2007

Citation: L. E. Bazilevich, “Hyperspace of Max-Plus Convex Compact Sets”, Mat. Zametki, 84:5 (2008), 658–666; Math. Notes, 84:5 (2008), 615–622

Citation in format AMSBIB
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\paper Hyperspace of Max-Plus Convex Compact Sets
\jour Mat. Zametki
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\pages 658--666
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\crossref{https://doi.org/10.4213/mzm4094}
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\transl
\jour Math. Notes
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\vol 84
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\pages 615--622
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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 L., Repovš D., Zarichnyi M., “Hyperspaces of max-plus convex subsets of powers of the real line”, J. Math. Anal. Appl., 394:2 (2012), 481–487  crossref  mathscinet  zmath  isi  scopus
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