From the preprint of my article “Filters on Posets and Generalizations” (with little rewording):
Definition 1. Let $latex \mathfrak{A}$ is a poset with least element $latex 0$. I will call elements $latex a$, $latex b$ in $latex \mathfrak{A}$ intersecting when exists c such that $latex c\ne 0$ and $latex c\subseteq a$ and $latex c\subseteq b$.
Today I’ve got the following idea:
We may drop the requirement that $latex \mathfrak{A}$ contains least element and change the requirement $latex c\ne 0$ to simple “$latex c$ is not the least element of $latex \mathfrak{A}$”.
This allows to generalize some of notions in my article.
I am going to rewrite both this article and my draft Pointfree funcoids to allow posets without least element.
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