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This article is cited in 2 scientific papers (total in 2 papers)
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.
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
Linking options:
https://www.mathnet.ru/eng/mzm4094https://doi.org/10.4213/mzm4094 https://www.mathnet.ru/eng/mzm/v84/i5/p658
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Abstract page: | 363 | Full-text PDF : | 157 | References: | 32 | First page: | 4 |
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