唯一弧连通连续统上紧群的每个连续作用都有不动点
Every continuous action of a compact group on a uniquely arcwise connected continuum has a fixed point
摘要：
我们正在处理的问题是否每个群或半群作用（具有某些附加性质）在一个连续统（具有某些附加性质）有一个不动点。2009年，Shi和Sun给出了其中一个结果。他们证明了在唯一弧连通连续统上的每一个幂零群作用都有一个不动点。我们正在寻找这种类型的结果，例如交换，紧凑或扭转群和半群作用于树突，树状，$λ$ -树状和唯一弧连接连续。证明了在唯一弧连通连续统上紧群或扭群的每个连续作用都有不动点。证明了紧致交换半群在唯一弧连通连续统或树连续统上的每个连续作用都有不动点。
英文摘要：
We are dealing with the question whether every group or semigroup action (with some additional property) on a continuum (with some additional property) has a fixed point. One of such results was given in 2009 by Shi and Sun. They proved that every nilpotent group action on a uniquely arcwise connected continuum has a fixed point. We are seeking for this type of results with e.g. commutative, compact or torsion groups and semigroups acting on dendrites, dendroids, $λ$-dendroids and uniquely arcwise connected continua. We prove that every continuous action of a compact or torsion group on a uniquely arcwise connected continuum has a fixed point. We also prove that every continuous action of a compact and commutative semigroup on a uniquely arcwise connected continuum or on a tree-like continuum has a fixed point.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
