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: Order embedding
Replies: 8   Last Post: Sep 16, 2013 10:01 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Victor Porton

Posts: 578
Registered: 8/1/05
Re: Order embedding
Posted: Sep 16, 2013 12:24 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

dullrich@sprynet.com wrote:

> On Mon, 16 Sep 2013 14:24:06 +0300, Victor Porton <porton@narod.ru>
> wrote:

>>William Elliot wrote:

>>> Let X,Y be (partially) ordered sets. Are these definitions correct?
>>> f:X -> Y is an order embedding when
>>> for all x,y, (x <= y iff f(x) <= f(y)).


> I think no. Surely an embedding is required to be injective.

>>> f:X -> Y is an order isomorphism when f is surjective
>>> and for all x,y, (x <= y iff f(x) <= f(y)).


> No. An isomorphism must be bijective.

Sorry, I was uncareful when answering William' question.

Dullrich is right.

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

[Privacy Policy] [Terms of Use]

© The Math Forum 1994-2015. All Rights Reserved.