On Efimov spaces and Radon measures |
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Authors: | Mirna D?amonja Grzegorz Plebanek |
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Institution: | a School of Mathematics, University of East Anglia, Norwich NR47TJ, UK b Institute of Mathematics, Wroc?aw University, 2/4 pl. Grunwaldzki, 50-384 Wroc?aw, Poland |
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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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Keywords: | 03E75 28E15 54G20 |
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