Connectedness and disconnectedness in pseudocompact groups
Connectedness and disconnectedness in pseudocompact groups
The author provides examples that settle natural questions about precompact and pseudocompact groups. Assuming Lusin's hypothesis -- \(2^\omega = 2^{\omega_1}\) -- he constructs (1) a totally minimal pseudocompact hereditarily disconnected Abelian group of covering dimension 1, and (2) for each \(n \in \mathbb{N}\) a totally minimal pseudocompact hereditarily disconnected Abelian group of covering dimension \(n\) that is not totally disconnected. -- Without Lusin's hypothesis one can get weaker examples of type 2; total minimality cannot be ensured.
- University of Udine Italy
disconnectedness, quasi-component; pseudocompact group; total disconenctedness, Structure of general topological groups, Counterexamples in general topology, covering dimension, pseudocompact groups, precompact group, Dimension theory in general topology, Topological groups (topological aspects)
disconnectedness, quasi-component; pseudocompact group; total disconenctedness, Structure of general topological groups, Counterexamples in general topology, covering dimension, pseudocompact groups, precompact group, Dimension theory in general topology, Topological groups (topological aspects)
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