# complete lattice

## Primary tabs

Defines:
countably complete lattice, countably-complete lattice, $\kappa$-complete, $\kappa$-complete lattice
Type of Math Object:
Definition
Major Section:
Reference

## Mathematics Subject Classification

### Countably complete semilattice

What's about a special name for the poset for which every countable subset has supremum? Could it be called "countably complete join-semilattice"? Or does it have any other special name?
--
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: Countably complete semilattice

porton writes:

> Could it be called "countably complete join-semilattice"?

Sounds good to me. But it's a rather obscure concept, so it's hard to find any examples of this term. I did find one example of "countably complete upper semilattice".

### Re: Countably complete semilattice

> porton writes:
>
> > Could it be called "countably complete join-semilattice"?
>
> Sounds good to me. But it's a rather obscure concept, so
> it's hard to find any examples of this term. I did find one
> example of "countably complete upper semilattice".

Googling of "countably complete upper semilattice" | "countably complete upper lattice" finds no results. Are there any standard term for countably complete semilattices?
--
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: Countably complete semilattice

Porton writes:

> Googling of "countably complete upper semilattice" |

Googling for "countably complete upper semilattice" gets one result if use Google Books ( http://books.google.com ) rather than the web search.

### Re: Countably complete semilattice

> Porton writes:
>
> > Googling of "countably complete upper semilattice" |
>
> Googling for "countably complete upper semilattice" gets one
> rather than the web search.

No on Google Books also zero search results.

Which book to you refer?

Finally, are there such the term, or maybe we should invent it?
--
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: Countably complete semilattice

porton writes:

> No on Google Books also zero search results.

Well, it works for me.

> Which book to you refer?

Recent Trends in Algebraic Development Techniques