Categorically closed topological groups

Abstract

Let $\mathcal{C}$ be a subcategory of the category of topologized semigroups and their partial continuous homomorphisms. An object $X$ of the category $\mathcal{C}$ is called $\mathcal{C}$-closed if for each morphism $f:X\to Y$ of the category $\mathcal{C}$ the image $f(X)$ is closed in $Y$. In the paper we detect topological groups which are $\mathcal{C}$-closed for the categories $\mathcal{C}$ whose objects are Hausdorff topological (semi)groups and whose morphisms are isomorphic topological embeddings, injective continuous homomorphisms, continuous homomorphisms, or partial continuous homomorphisms with closed domain.

26 pages

References in corpus (5)

• On H-closed paratopological groups
• On linearly ordered $H$-closed topological semilattices
• Completeness and absolute $H$-closedness of topological semilattices
• $H$-closed quasitopological groups
• A quantitative generalization of Prodanov-Stoyanov Theorem on minimal Abelian topological groups

Cited by in corpus (5)

• Characterizing chain-compact and chain-finite topological semilattices
• Completeness and absolute $H$-closedness of topological semilattices
• Characterizing categorically closed commutative semigroups
• A quantitative generalization of Prodanov-Stoyanov Theorem on minimal Abelian topological groups
• C-Minimal topological groups