The completeness of free Boolean topological groups
Ol'ga V. Sipacheva, Mikhail G. Tkachenko
TL;DR
This paper establishes that the Weil completeness of free Boolean topological groups on Tychonoff spaces is equivalent to the Dieudonné completeness of the underlying space, answering a question from 2015.
Contribution
It proves a necessary and sufficient condition linking the completeness of free Boolean topological groups to the Dieudonné completeness of the base space.
Findings
Weil completeness of B(X) iff X is Dieudonné complete
Provides a positive answer to a 2015 open question
Establishes a precise characterization of completeness in free Boolean groups
Abstract
It is proved that the free Boolean topological group on a Tychonoff space is Weil complete if and only if the space is Dieudonn\'e complete. This result provides a positive answer to a question posed by the first listed author in 2015.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Rings, Modules, and Algebras · Advanced Algebra and Logic