Symmetric and strongly symmetric homeomorphisms on the real line with non-symmetric inversion

Huaying Wei; Katsuhiko Matsuzaki

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arXiv · 1905.05933

Symmetric and strongly symmetric homeomorphisms on the real line with non-symmetric inversion

Huaying Wei·Katsuhiko Matsuzaki

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Abstract

We show an example of a symmetric homeomorphism $h$ of the real line $\mathbb{R}$ onto itself such that $h^{-1}$ is not symmetric. This implies that the set of all symmetric self-homeomorphisms of $\mathbb{R}$ does not constitute a group under the composition. We also deal with strongly symmetric self-homeomorphisms of $\mathbb{R}$ along the same line. These results reveal the difference of the sets of such self-homeomorphisms of the real line from those of the unit circle.

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Huaying Wei, Katsuhiko Matsuzaki. 2019-05-15. Symmetric and strongly symmetric homeomorphisms on the real line with non-symmetric inversion. https://arxiv.org/abs/1905.05933

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