论文标题
寄生的细菌
Germs in a poset
论文作者
论文摘要
由通讯函数理论的启发，我们在有限的poset中介绍了{\ em grem}的概念，以及poset的{\ em grem扩展}的概念。我们表明，任何有限的POSET都承认了最大的细菌扩展名，称为其{\ em Germ Closure}。我们说，如果$ u $的细菌自然嵌入$ t $，则有限晶格$ t $的子集$ u $是$ t $中的{\ em germ gregsible}。我们表明，对于有限晶格$ t $的任何子集$ s $的任何子集，都有一个唯一的可扩展子集$ u $的$ t $ $ t $，以至于$ u \ u \ subseteq s \ subseteq \ overline {g} $
Motivated by the theory of correspondence functors, we introduce the notion of {\em germ} in a finite poset, and the notion of {\em germ extension} of a poset. We show that any finite poset admits a largest germ extension called its {\em germ closure}. We say that a subset $U$ of a finite lattice $T$ is {\em germ extensible} in $T$ if the germ closure of $U$ naturally embeds in $T$. We show that any for any subset $S$ of a finite lattice $T$, there is a unique germ extensible subset $U$ of $T$ such that $U\subseteq S\subseteq \overline{G}(U)$, where $\overline{G}(U)\subseteq T$ is the embedding of the germ closure of $U$.
