Conditions of Cantor and Co-Cantor Properties for Acts over the Trivial Semigroup
Игорь Борисович Кожухов, A. S. Sotov · Russian Mathematics · 2025
We find the necessary and sufficient conditions for an act $$X$$ over a trivial semigroup $$\{ e\} $$ to be Cantor (or co-Cantor), that is, for any act $$Y$$ the existence of injective (respectively, surjective) homomorphisms $$X \to Y$$ and $$Y \to X$$ implies the isomorphism $$X \cong Y$$ .