论文标题
拓扑，poset和有限的难题
Topologies, Posets and Finite Quandles
论文作者
论文摘要
Alexandroff空间是一个拓扑空间，在该空间中，开放式设置的每个交叉点都打开。 AlexandRoff $ T_0 $空间与部分有序集（POSETS）之间有一对一的对应关系。我们调查了有限问题的Alexandroff $ T_0 $ TOPOGOLIES。我们证明，当且仅当Quandle具有多个轨道时，在有限的Quandle上有一个非平凡的拓扑结构。此外，我们表明，具有$ n $ orbits的Quandles上的正确连续posets为$ n $ - 分支机构。我们还发现，对于偶尔的二面地块，所有可能的拓扑的数量使正确的乘法连续。最多提供了五个基础性问题的一些明确计算。
An Alexandroff space is a topological space in which every intersection of open sets is open. There is one to one correspondence between Alexandroff $T_0$-spaces and partially ordered sets (posets). We investigate Alexandroff $T_0$-topologies on finite quandles. We prove that there is a non-trivial topology on a finite quandle making right multiplications continuous functions if and only if the quandle has more than one orbit. Furthermore, we show that right continuous posets on quandles with $n$ orbits are $n$-partite. We also find, for the even dihedral quandles, the number of all possible topologies making the right multiplications continuous. Some explicit computations for quandles of cardinality up to five are given.
