Metrizability of Pixley-Roy hyperspaces (Q794311)
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scientific article; zbMATH DE number 3859962
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Metrizability of Pixley-Roy hyperspaces |
scientific article; zbMATH DE number 3859962 |
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Metrizability of Pixley-Roy hyperspaces (English)
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1983
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The main result is that the Pixley-Roy hyperspace of a space X is metrizable iff it is a closed image of a metrizable space iff it is a paracompact p-space (it follows from the proof that the p-space property can be replaced by the property of being of pointwise countable type). Similar characterizations for the hyperspace to be an \(M_ 1\)-space or a Moore space are given. Furthermore, the situation when X satisfies some additional assumptions is considered.
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GO-spaces
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Pixley-Roy hyperspace
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paracompact p-space
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\(M_ 1\)-space
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Moore space
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0.89499927
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0.8823364
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0.8756064
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0.87544805
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