论文标题
专业半层次的通用扩展
Universal extensions of specialization semilattices
论文作者
论文摘要
专业半静脉曲张是连接的半纹身，以及满足适当兼容性条件的较粗糙的预订$ \ sqsubseteq $。如果$ x $是拓扑空间，则$（\ Mathcal P（x），\ cup，\ sqsubseteq）$是一种专业化半层次，其中$ x \ sqsubseteq y $如果$ x \ subseteq ky $，则适用于$ x，y \ subseteq x $，以及$ k $ k $。 专业的半纹身和POSET在许多不同的科学领域中以辅助结构的形式出现，甚至与拓扑无关。简而言之，该概念很有用，因为它允许我们考虑“被“生成”的关系，而无需需要存在实际的“闭合”或“船体”，这在某些情况下可能会出现问题。 在一项以前的工作中，我们表明，每个专业半都可以嵌入与上述拓扑空间相关的专业半静脉内。在这里，我们描述了专业半静脉曲张中的普遍嵌入到加性闭合半层次中。我们注意到，一个分类论点保证了在许多平行情况下普遍嵌入的存在。
A specialization semilattice is a join semilattice together with a coarser preorder $ \sqsubseteq $ satisfying an appropriate compatibility condition. If $X$ is a topological space, then $(\mathcal P(X), \cup, \sqsubseteq )$ is a specialization semilattice, where $ x \sqsubseteq y$ if $x \subseteq Ky$, for $x,y \subseteq X$, and $K$ is closure. Specialization semilattices and posets appear as auxiliary structures in many disparate scientific fields, even unrelated to topology. For short, the notion is useful since it allows us to consider a relation of "being generated by" with no need to require the existence of an actual "closure" or "hull", which might be problematic in certain contexts. In a former work we showed that every specialization semilattice can be embedded into the specialization semilattice associated to a topological space as above. Here we describe the universal embedding of a specialization semilattice into an additive closure semilattice. We notice that a categorical argument guarantees the existence of universal embeddings in many parallel situations.
