关于双环幺半群的拓扑关联
On semitopological interassociates of the bicyclic monoid
摘要：
研究了双环半群$\mathscr{C}(p,q)$的半拓扑关联$\mathscr{C}_{m,n}$.特别地，我们证明了对于任意非负整数$m$，$n$和$\mathscr{C}_{m,n}$上的每个Hausdorff拓扑$τ$，使得$\left(\mathscr{C}_{m,n},τ\right)$是一个拓扑半群，都是离散的.证明了如果双圈幺半群$\mathscr{C}_{m,n}$的一个关联是Hausdorff拓扑半群$(S,\cdot)$和$I=S\setminus\mathscr{C}_{m,n}\neq\varnothing$的稠密子半群，则$I$是半群$S$的双边理想，并证明了对任意非负整数$m$，$n$，任何Hausdorff局部紧拓扑半群$\mathscr{C}_{m,n}^0=\mathscr{C}_{m,n}\sqcup\{0\}$是离散的或紧的.
英文摘要：
Semitopological interassociates $\mathscr{C}_{m,n}$ of the bicyclic semigroup $\mathscr{C}(p,q)$ are studied. In particular, we show that for arbitrary non-negative integers $m$, $n$ and every Hausdorff topology $τ$ on $\mathscr{C}_{m,n}$ such that $\left(\mathscr{C}_{m,n},τ\right)$ is a semitopological semigroup, is discrete. Also, we prove that if an interassociate of the bicyclic monoid $\mathscr{C}_{m,n}$ is a dense subsemigroup of a Hausdorff semitopological semigroup $(S,\cdot)$ and $I=S\setminus\mathscr{C}_{m,n}\neq\varnothing$ then $I$ is a two-sided ideal of the semigroup $S$ and show that for arbitrary non-negative integers $m$, $n$, any Hausdorff locally compact semitopological semigroup $\mathscr{C}_{m,n}^0=\mathscr{C}_{m,n}\sqcup\{0\}$ is either discrete or compact.
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