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.
Clontzet al., π-Base: a community database of topological counterexamples, https:// topology.pi-base.org/
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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.