The Extended Real Line with Reentry is the first compact path-connected US-not-KC space, obtained via a density-modified quotient of the extended reals.
Brauer groups of genus zero extensions of number fields
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
We determine the isomorphism class of the Brauer groups of certain nonrational genus zero extensions of number fields. In particular, for all genus zero extensions E of the rational numbers Q that are split by Q(\sqrt{2}), Br(E) is isomorphic to Br(Q(t)).
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2026 1verdicts
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The Extended Real Line with Reentry: Separating US from KC in the Clontz Hierarchy
The Extended Real Line with Reentry is the first compact path-connected US-not-KC space, obtained via a density-modified quotient of the extended reals.