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atom

Defines: 
atomic poset, atomic lattice, atomistic lattice, atomistic
Type of Math Object: 
Definition
Major Section: 
Reference
Groups audience: 

Mathematics Subject Classification

06A06 no label found06B99 no label found

Comments

It seems that the term "point lattice" is sometimes used in the same sense as "atomistic lattice" as defined here. Should put a note about this terminology.
Victor Porton - http://www.mathematics21.org
* Algebraic General Topology and Math Synthesis
* 21 Century Math Method (post axiomatic math logic)
* Category Theory - new concepts

Can you give me some references as to where "point lattice" is used?

I have found a Russian term in Russian book.
An online dictionary has translated this term
as ``point lattice''. (I assume that the online
dictionary http://lingvo.yandex.ru knows what
it says because it has a translation for
whole two-words term, not ``point'' separately
and ``lattice'' separately.)

It seems that ``point lattice'' is the same
as ``atomistic lattice''. Both terms are rare.
What's our choice?
Victor Porton - http://www.mathematics21.org
* Algebraic General Topology and Math Synthesis
* 21 Century Math Method (post axiomatic math logic)
* Category Theory - new concepts

> It seems that ``point lattice'' is the same
> as ``atomistic lattice''. Both terms are rare.
> What's our choice?

Unfortunately, using an online dictionary is not an
optimal way to translate mathematical terminology.

The term ``atomistic lattice'' is defined in Gr\"atzer's book
(General Lattice Theory). For a fairly recent example of an
article using the term, consult:

F. Wehrung, A uniform refinement property for congruence
lattices, Proc. Amer. Math. Soc. 127 (1999), 363--370.

The only references to ``point lattices'' I've been able
to find so far are talking about the kind of lattices that
consist of regularly-spaced points in some Euclidean space.

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