Symmetric and strongly symmetric homeomorphisms on the real line with non-symmetric inversion
Symmetric and strongly symmetric homeomorphisms on the real line with non-symmetric inversion
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DOI：
10.1007/s13324-021-00510-7
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发表时间：
2019-05
影响因子：
1.7
通讯作者：
Huaying Wei;Katsuhiko Matsuzaki
中科院分区：
文献类型：
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作者：
Huaying Wei;Katsuhiko Matsuzaki
一个拟对称同胚定义了一个全称teichm<e:1>空间的元素，一个对称元素属于它的子空间。我们给出了实直线对自身对称的非对称同胚的一个例子。这意味着在复合下，所有的对称自同胚的集合不构成群。我们还考虑了一个强对称自同胚的相同问题，该问题是由调和分析的某个概念定义的。这些结果揭示了实直线的自同胚集与单位圆的自同胚集的区别。
A quasisymmetric homeomorphism defines an element of the universal Teichmüller space and a symmetric one belongs to its little subspace. We show an example of a symmetric homeomorphismhof the real lineonto itself such thatis not symmetric. This implies that the set of all symmetric self-homeomorphisms ofdoes not constitute a group under the composition. We also consider the same problem for a strongly symmetric self-homeomorphism ofwhich is defined by a certain concept of harmonic analysis. These results reveal the difference of the sets of such self-homeomorphisms of the real line from those of the unit circle.