Homeomorphism groups on the positive real numbers defined by binary operations

被引：0

作者：

Takahasi, Sin-Ei ^{[1
]}

机构：

[1] Yamagata Univ, Natsumidai 3 8 16 502, Funabashi, Chiba 2730866, Japan

来源：

SEMIGROUP FORUM | 2023年 / 107卷 / 03期

关键词：

Homeomorphism group; Binary operation; Cancellative continuous semigroup operation;

D O I：

10.1007/s00233-023-10395-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a continuous binary operation * on the positive real numbers R+ with ordinary topology, we consider the homeomorphism group Homeo(*)(R+) consisting of all homeomorphisms on R+ which preserve *. We show that if * is any continuous cancellative semigroup operation on R+, then Homeo(*)(R+) is isomorphic to either one of the three well-known groups. Furthermore, we reveal homeomorphism groups defined by some continuous noncancellative semigroup operations on R+.

引用

页码：780 / 791

页数：12

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