2022/07/29 by Banakh, Taras
#20M18 #22A15 #54B30 #54D35 #54H11 #54H12 #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2208.00074
A semigroup X is absolutely (resp. injectively) T1S-closed if for any (injective) homomorphism h:X→ Y to a T1 topological semigroup Y∈\mathcal C, the image h[X] is closed in Y. We prove that a commutative semigroup X is injectively T1S-closed if and only if X is bounded, nonsingular and Clifford-finite. Using this characterization, we prove that (1) every injectively T1S-closed semigroup has injectively T1S-closed center, and (2) every absolutely T1S-closed semigroup has finite center.