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.independent

Topic: Homomorphism of posets and lattices
Replies: 16   Last Post: Sep 20, 2013 6:22 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
William Elliot

Posts: 1,436
Registered: 1/8/12
Homomorphism of posets and lattices
Posted: Sep 18, 2013 12:20 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

What's your opinion about the following except from a manuscript?

I consider the Definition 2.92 to be in error unless the domain
of the function is a linear order. For example, the identity
function from a two point antichain { a,b } to the chain a < b.

Comments? Are not antichains preserved by order isomorphisms?

2,1,12 Homomorphism of posets and lattices

Definition 2.90. A monotone function (also called order homomorphism) from
a poset A to a poset B is such a function f that x <= y --> f(x) <= f(y).

Definition 2.91. Order embedding is an injective monotone function.

Definition 2.92. Order isomorphism is an surjective order embadding
(= bijective monotone function).

Order isomorphism preserves properties of posets, such as
order, joins and meets, etc.

Definition 2.93.



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.