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Re: Order embedding from a poset into a complete lattice
Posted:
Dec 30, 2012 7:10 PM


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 DedekindMacNeille 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".



