局部紧拓扑多环幺半群的分类
Classifying locally compact semitopological polycyclic monoids
摘要：
我们提出了一个完整的分类Hausdorff局部紧多环幺半群的拓扑同构。{ \em多环幺半群}是由子集$Λ$生成的具有零的逆幺半群，使得对于任何$x\inΛ$为$xx^{-1}=1$，对于任何不同的$x,y\inΛ$为$xy^{-1}=0$。证明了多环幺半群$M$上任何具有连续位移的非离散Hausdorff局部紧拓扑与离散空间$M\setminus\{0\}$的一点紧化拓扑一致.
英文摘要：
We present a complete classification of Hausdorff locally compact polycyclic monoids up to a topological isomorphism. A {\em polycyclic monoid} is an inverse monoid with zero, generated by a subset $Λ$ such that $xx^{-1}=1$ for any $x\inΛ$ and $xy^{-1}=0$ for any distinct $x,y\inΛ$. We prove that any non-discrete Hausdorff locally compact topology with continuous shifts on a polycyclic monoid $M$ coincides with the topology of one-point compactification of the discrete space $M\setminus\{0\}$.
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