All Questions

We have established the following result regarding the Dushnik–Miller dimension of posets. Let $P$ be a poset with downsets $C, D \subseteq P$. If the dimensions of $C$ and $D$ are $m$ and $n$, ...

Let $L$ be a finite (upper) semimodular lattice. Recall that this means $L$ is graded and its rank function $\rho\colon L \to \mathbb{N}$ satisfies $$ \rho(x) + \rho(y) \geq \rho(x\vee y)+\rho(x \...

I say that a relation $R$ on a poset $P$ is downward closed if for each $(x,y)\in R$, and $x'\le x$, then $(x',y)\in R$. Is there a reference where this thing is studied, maybe under a different name? ...

How are called in combinatorics monotone maps of partially ordered sets such that the image of a lower set is a lower set, i.e. closed (or open) maps of finite topologies? Is there a classification ...