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Infinite-dimensional hyperspaces of convex bodies of constant width
Bazylevych, Lidia ; Zarichnyi, Michael, 1958-
There exists a natural embedding of the hyperspace of compact convex bodies of constant width in ▫$\mathbb{R}^n$▫ into those of ▫$\mathbb{R}^{n+1}$▫. This allows us to consider the hyperspace of ...compact convex bodies of constant width in the space ▫$\mathbb{R}^\infty = \varinjlim \mathbb{R}^n$▫. We prove that this hyperspace is homeomorphic to ▫$Q^\infty = \varinjlim Q^n$▫, where ▫$Q$▫ denotes the Hilbert cube.
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