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Topic: Homomorphism of posets and lattices
Replies: 16   Last Post: Sep 20, 2013 6:22 AM

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Victor Porton

Posts: 520
Registered: 8/1/05
Re: Homomorphism of posets and lattices
Posted: Sep 19, 2013 10:13 AM
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William Elliot wrote:

> Now that those definitions have finally been corrected,
> I've found yet another error to bring to your attention.
>
> Proposition 3.4. Let f be a monotone map from a meet-semilattice K
> to some poset L. If
> Aa,b in K: f(a meet b) = f(a) meet f(b)
> then f is a straight map.
>
> The problem I see with this proposition is that
> f(a) meet f(b) doesn't exist for a,b in K.
>
> I suggest these corrections.
>
> Let f be a monotone map from a meet-semilattice K to some meet-semilattice
> L.
>
> Let f be a monotone map from a meet-semilattice K to some poset L
> for which f(K) is a meet-semilattice.
>
> Comments or suggestions anyone?


I've uploaded a new version of my preprint with:

Let f be a monotone map from a meet-semilattice A to a meet-semilattice B.



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