## The Topology on a Complete Semilattice

**Authors:** Max Null, Sergey Belov

We define the topology atop(χ) on a complete upper semilattice χ = (M, ≤).
The limit points are determined by the formula
lim (X) = sup{a ∈ M | {x ∈ X| a ≤ x} ∈ D},
D
where X ⊆ M is an arbitrary set, D is an arbitrary non-principal ultrafilter
on X. We investigate lim (X) and topology atop(χ) properties. In particular,
D
we prove the compactness of the topology atop(χ).

**Comments:** 23 Pages.

**Download:** **PDF**

### Submission history

[v1] 2016-08-29 10:19:42

[v2] 2016-09-14 08:54:47

[v3] 2016-11-03 03:06:10

**Unique-IP document downloads:** 53 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*