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

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Victor Porton

Posts: 529
Registered: 8/1/05
Re: Order embedding
Posted: Sep 16, 2013 12:24 PM
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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)).

>>
>>Yes.

>
> 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)).

>>
>>Yes.

>
> No. An isomorphism must be bijective.


Sorry, I was uncareful when answering William' question.

Dullrich is right.



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