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

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 ]
quasi

Posts: 10,451
Registered: 7/15/05
Re: Homomorphism of posets and lattices
Posted: Sep 18, 2013 2:18 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

quasi <quasi@null.set> wrote:
>
>Victor Porton wrote:

>>
>>I've corrected the definitions:
>>
>>Definition 1. A monotone function (also called order
>>homomorphism) from a poset A to a poset B is such a function f
>>that x<=y -> fx<=fy.
>>
>>Definition 2. Order embedding is an monotone function whose
>>inverse is also monotone.

>
>Not quite right.
>
>To have an inverse, it would have to be bijective.
>
>Instead, try this (Wikipedia's version):
>
>Given posets X,Y, a function f:X -> Y is called an order
>embedding if (x <= y iff f(x) <= f(y)).


A better choice of letters:

Given posets A,B, a function f:A -> B is called an order
embedding if (x <= y iff f(x) <= f(y)).

>>Obvious 3. Order embeddings are always injective.
>
>Yes.
>

>>Definition 4. Order isomorphism is a surjective order embedding.
>
>Yes, that's Wiki's definition.


quasi



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.