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Every continuous action of a compact group on a uniquely arcwise connected continuum has a fixed point. (arXiv:1709.00852v2 [math.DS] UPDATED)
来源于:arXiv
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, $\lambda$-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 has a fixed point. 查看全文>>