Skip to content
January 14, 2011 / porton

Intersecting elements of posets without least element

From the preprint of my article “Filters on Posets and Generalizations” (with little rewording):

Definition 1. Let \mathfrak{A} is a poset with least element 0. I will call elements a, b in \mathfrak{A} intersecting when exists c such that c\ne 0 and c\subseteq a and c\subseteq b.

Today I’ve got the following idea:

We may drop the requirement that \mathfrak{A} contains least element and change the requirement c\ne 0 to simple “c is not the least element of \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.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this: