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




Re: Order embedding
Posted:
Sep 16, 2013 12:24 PM


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.



