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2
votes
1
answer
259
views
What lattices are isomorphic to $R^{N}$ for some $N$, equipped with the product order?
What lattices are isomorphic to $\mathbb{R}^{N}$ for some $N\in \mathbb{N}$, equipped with the canonical order?
Remark:
When I say $\mathbb{R}^N$, I don’t mean it to be a vector space. Instead, I r …
3
votes
1
answer
215
views
Embedding of a poset with "desirable" characteristics
Let $(P, \succeq)$ be a poset (you can assume $\succeq$ is not empty). I am interested in finding a poset $(X, \succeq^*)$ that embeds $(P, \succeq)$, and $\forall x,y \in X$ both of the following pro …
4
votes
2
answers
449
views
Is every finite poset a subset of a finite complemented distributive lattice?
Let $(X,\succeq)$ be a poset. I have the following two questions:
Is it true that there exists a finite complemented distributive lattice (a Boolean lattice) $(S, \succeq^*)$ such that $X\subseteq S$ …