Measures on minimally generated Boolean algebras |
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Authors: | Piotr Borodulin-Nadzieja |
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Affiliation: | Instytut Matematyczny, Uniwersytet Wroc?awski, pl. Grunwaldzki 2/4, 50-384 Wroc?aw, Poland |
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Abstract: | We investigate properties of minimally generated Boolean algebras. It is shown that all measures defined on such algebras are separable but not necessarily weakly uniformly regular. On the other hand, there exist Boolean algebras small in terms of measures which are not minimally generated. We prove that under CH a measure on a retractive Boolean algebra can be nonseparable. Some relevant examples are indicated. Also, we give two examples of spaces satisfying some kind of Efimov property. |
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Keywords: | 54G20 28C15 06F30 |
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