论文标题
通用专业化半纹身
Universal specialization semilattices
论文作者
论文摘要
A specialization semilattice is a structure which can be embedded into $(\mathcal P(X), \cup, \sqsubseteq )$, where $X$ is a topological space, $ x \sqsubseteq y$ means $x \subseteq Ky$, for $x,y \subseteq X$, and $K$ is closure in $X$.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。 通常，在专业半静脉曲张中，闭合是不可表达的。另一方面，我们证明，每个专业半静脉曲张都可以嵌入到“主要”专业半层次中，实际上可以在其中定义封闭。
A specialization semilattice is a structure which can be embedded into $(\mathcal P(X), \cup, \sqsubseteq )$, where $X$ is a topological space, $ x \sqsubseteq y$ means $x \subseteq Ky$, for $x,y \subseteq X$, and $K$ is closure in $X$. Specialization semilattices and posets appear as auxiliary structures in many disparate scientific fields, even unrelated to topology. In general, closure is not expressible in a specialization semilattice. On the other hand, we show that every specialization semilattice can be canonically embedded into a "principal" specialization semilattice in which closure can be actually defined.
