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Limit points at infinity for semigroup compactification classification
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DOI：10.1007/s00233-026-10643-5.png)
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Abstract
En 中文
This paper investigates compactifications of a semitopological semigroup S, focusing on the relationship between psi(A)(infinity), the set of limit points of psi at infinity for a non-precompact subset A subset of S, and the minimal ideal K(X) in a semigroup compactification (psi, X) of S. It is shown that psi(A)(infinity) may form an ideal or subgroup under precompact conditions on A and continuity conditions on X. Consequently, a classification of semigroup compactifications that are factors of a subdirect product of the one-point and group compactifications is provided. Additionally, the paper examines topological semigroup compactifications for a broad class of subsemigroups of complete totally ordered groups, correcting and generalizing Example 3.2.4 from "Analysis on semigroups" by J. F. Berglund, D. H. Junghenn, and P. Milnes (Wiley, New York (1989)) and discussing applications to the Bohr compactification.
Keywords:
Semitopological semigroup
Minimal ideal of a semigroup
Semigroup compactification
Factor of a semigroup compactification
Subdirect product of semigroup compactifications
One-point Alexandroff compactification
Bohr compactification
Ordered group