# atom

## Primary tabs

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

## Mathematics Subject Classification

### Point lattices

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

### Re: Point lattices

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

### Re: Point lattices

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

### Re: Point lattices

> 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.