3
$\begingroup$

According to this wiki page, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet).

Whereas, the wiki page of complete partial order does not give a clear definition of complete partial order.

What is the definition of complete partial order?

Additionally, what is the difference between complete partial order and Complete lattice?

$\endgroup$
5
$\begingroup$

The page gives the definition. It says that an $\omega$-complete partial order (complete partial order), is one where every increasing chain of order type $\omega$ has a supremum.

Now the difference between a complete partial order and a complete lattice should be clear. One only talks about particular chains; the other one talks about any subset.

| cite | improve this answer | |
$\endgroup$
1
$\begingroup$

Look at it this way: in a complete lattice you have more supremum relations (one for each subset). While in a partially ordered set you only have supremum of subsets of a chain (in a cahin all elements are comparable).

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.