On Loeb and weakly Loeb Hausdorff spaces (Q2731710)
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scientific article; zbMATH DE number 1626390
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Loeb and weakly Loeb Hausdorff spaces |
scientific article; zbMATH DE number 1626390 |
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15 April 2002
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On Loeb and weakly Loeb Hausdorff spaces (English)
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A topological space is (weakly) Loeb, if there is a (multiple) choice function on the family of its none-empty closed subsets. This property is an essential premise of Loeb's proof of the Tikhonov theorem. The authors show that the following assertions depend on the axiom of choice (AC): (i) The product of weakly Loeb Hausdorff spaces is weakly Loeb. By theorem 2.4 this assertion implies van Douwen's axiom LN. (ii) Compact Hausdorff spaces are weakly Loeb.
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