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arXiv · 0804.3645

The diffeomorphism groups of the real line are pairwise bihomeomorphic

Taras Banakh·Tatsuhiko Yagasaki
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Abstract

We prove that the group D^r(R) of C^r diffeomorphisms of the real line, endowed with the compact-open and Whitney C^r topologies, is bihomeomorphic to the group H(R) of homeomorphisms of the real line endowed with the compact-open and Whitney topologies. This implies that the diffeomorphism group D^r(R) endowed with the Whitney C^r topology is homeomorphic to the countable box-power of the separable Hilbert space.

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Taras Banakh, Tatsuhiko Yagasaki. 2009-11-03. The diffeomorphism groups of the real line are pairwise bihomeomorphic. https://arxiv.org/abs/0804.3645

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