Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.research

Topic: Order Embeddings
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
William Elliot

Posts: 1,528
Registered: 1/8/12
Order Embeddings
Posted: Jan 19, 2014 8:13 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Let (S,<=) be an (partially) ordered set and A a subset
of S with the inherited order, namely, <= /\ AxA

Thus, A is order embedded in S.

When S isn't a lattice and A is a lattice would would you
call these cases?

A has the inherited order.

For all a,b in A, a inf_S b and a sup_S b exist and additionally
a inf_S b = a inf_A b and a sup_S b = a sup_A b.  Note that because
of those requirements A has the inherited order.

For all a,b in A, if a inf_S b exists, then a inf_S b = a inf_A b
and if a sup_S b exist, a sup_S b = a sup_A b.

I'd call them respectively:
an order embedding of an ordered subset that happens to be a lattice;
an embedding of lattice;
a pseudo lattice embedding.

How would you describe these three distinctions?
Do some already have terms that describe them?
What use are they?  Have you an example or two?

I'd think the 2nd would be the useful one,
the others of little or no significance.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.