Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4661226 | Topology and its Applications | 2007 | 10 Pages |
Abstract
We give a construction under CH of an infinite Hausdorff compact space having no converging sequences and carrying no Radon measure of uncountable type. Under ⋄ we obtain another example of a compact space with no convergent sequences, which in addition has the stronger property that every nonatomic Radon measure on it is uniformly regular. This example refutes a conjecture of Mercourakis from 1996 stating that if every measure on a compact space K is uniformly regular then K is necessarily sequentially compact.
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Physical Sciences and Engineering
Mathematics
Geometry and Topology