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Topic: Order embedding from a poset into a complete lattice
Replies: 2   Last Post: Dec 30, 2012 7:29 PM

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Butch Malahide

Posts: 894
Registered: 6/29/05
Re: Order embedding from a poset into a complete lattice
Posted: Dec 30, 2012 7:10 PM
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On Dec 30, 12:40 pm, Victor Porton <por...@narod.ru> wrote:
> I asked this question athttp://math.stackexchange.com but received no
> answer.
>
> Let A is an arbitrary poset.
>
> Does it necessarily exist an order embedding from A into some complete
> lattice B, which preserves all suprema and infima defined in A?


Yes, the Dedekind-MacNeille completion of A has this property.

https://en.wikipedia.org/wiki/Dedekind%E2%80%93MacNeille_completion

By the way, there are two grammatical errors in your post. For "Let A
is" read "Let A be". For "Does it necessarily exist" read "Does there
necessarily exist".



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