Zero-Dimensionality of Some Pseudocompact Groups
Copyright policy )Zero-Dimensionality of Some Pseudocompact Groups
We prove that hereditarily disconnected countably compact groups are zero-dimensional. This gives a strongly positive answer to a question of Shakhmatov. We show that hereditary or total disconnectedness yields zero-dimensionality in various classes of pseudocompact groups.
- University of Udine Italy
Connected and locally connected spaces (general aspects), pseudocompact group; zero-dimensional group; countably comapct group, Compactness, connected group, quasi-component, zero-dimensional group, Dimension theory in general topology, connected component, totally minimal group, Structure of general topological groups, totally disconnected topological group, torsion group, hereditarily pseudocompact group, countably compact group, total disconnectedness, zero-dimensionality, ``\(P\)-minimal'' and ``\(P\)-closed'' spaces, hereditarily disconnected group
Connected and locally connected spaces (general aspects), pseudocompact group; zero-dimensional group; countably comapct group, Compactness, connected group, quasi-component, zero-dimensional group, Dimension theory in general topology, connected component, totally minimal group, Structure of general topological groups, totally disconnected topological group, torsion group, hereditarily pseudocompact group, countably compact group, total disconnectedness, zero-dimensionality, ``\(P\)-minimal'' and ``\(P\)-closed'' spaces, hereditarily disconnected group
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