2022/07/29 by Тарас Банах, Banakh, Taras, Myroslava Vovk +1
Computer Science · Decision Sciences · Mathematics · #20M18 #22A15 #54B30 #54D35 #54H11 #54H12 #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2208.00072
openalex publication_date 2022/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathcal C be a class of T1 topological semigroups, containing all Hausdorff zero-dimensional topological semigroups. A semigroup X is \mathcal C-closed if X is closed in any topological semigroup Y∈\mathcal C that contains X as a discrete subsemigroup; X is injectively \mathcal C-closed if for any (injective) homomorphism h:X→ Y to a topological semigroup Y∈\mathcal C, the image h[X] is closed in Y. A semigroup X is unipotent if it contains a unique idempotent. We prove that a unipotent commutative semigroup X is (injectively) \mathcal C-closed if and only if X is bounded, nonsingular (and group-finite). This characterization implies that for every injectively \mathcal C-closed unipotent semigroup X, the center Z(X) is injectively \mathcal C-closed.