关于变换幺半群的自动同胚性
On automatic homeomorphicity for transformation monoids
摘要：
变换幺半群带有一个典型拓扑-逐点收敛拓扑。一个闭变换幺半群$\mathfrak{M}$被称为关于一个结构类$\mathcal{K}$具有自动同胚性，如果$\mathfrak{M}$到$\mathcal{K}$的一个成员的自同态幺半群的每个幺半群同构自动是同胚。本文证明了有理数上的非减函数幺半群、Urysohn空间上的非扩张函数幺半群和可数泛齐次偏序集的自同态幺半群的自动同胚性。
英文摘要：
Transformation monoids carry a canonical topology --- the topology of point-wise convergence. A closed transformation monoid $\mathfrak{M}$ is said to have automatic homeomorphicity with respect to a class $\mathcal{K}$ of structures, if every monoid-isomorphism of $\mathfrak{M}$ to the endomorphism monoid of a member of $\mathcal{K}$ is automatically a homeomorphism. In this paper we show automatic homeomorphicity-properties for the monoid of non-decreasing functions on the rationals, the monoid of non-expansive functions on the Urysohn space and the endomorphism-monoid of the countable universal homogeneous poset.
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