## 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.

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### Submission history

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

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

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

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