论文标题
关于紧凑型公制空间上的反向半群$γ（x）$的波兰$ x $
On the Polishness of the inverse semigroup $Γ(X)$ on a compact metric space $X$
论文作者
论文摘要
令$γ（x）$为紧凑型公制空间$ x $的开放子集之间的部分同构的反向半群。有一个拓扑，表示为$τ_{hco} $，它使$γ（x）$成为拓扑反向半群。我们解决了$τ_{hco} $是抛光的问题。对于0维紧凑的度量空间$ x $，我们证明$（γ（x），τ_{hco}）$是抛光的，是通过证明它对波兰对称对称性逆向半群的封闭子群的拓扑同构是同构的。我们介绍了类似于古典Munn Semigroups的示例，这些示例是在开放式集合的晶格上由部分同构的波兰反向半群。
Let $Γ(X)$ be the inverse semigroup of partial homeomorphisms between open subsets of a compact metric space $X$. There is a topology, denoted $τ_{hco}$, that makes $Γ(X)$ a topological inverse semigroup. We address the question of whether $τ_{hco}$ is Polish. For a 0-dimensional compact metric space $X$, we prove that $(Γ(X), τ_{hco})$ is Polish by showing that it is topologically isomorphic to a closed subsemigroup of the Polish symmetric inverse semigroup $I(\N)$. We present examples, similar to the classical Munn semigroups, of Polish inverse semigroups consisting of partial isomorphism on lattices of open sets.
