Set Theory and Logic


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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