The semi-Polish theorem: one-sided vs joint continuity in groups (Q387915)
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scientific article; zbMATH DE number 6239000
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The semi-Polish theorem: one-sided vs joint continuity in groups |
scientific article; zbMATH DE number 6239000 |
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The semi-Polish theorem: one-sided vs joint continuity in groups (English)
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17 December 2013
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A right invariant metric on a group \(X\) is a mapping with the property \(d(xv,yv)=d(x,y)\) for all \(x,y,v\) in \(X\). Groups with such metrics are studied and it is shown that if a space \(X\) equipped with such a metric is non-meagre and semi-analytic, then it is a Polish topological group. Implications for proper metric spaces with right-invariant metric are shown.
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automatic continuity
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analytic Baire theorem
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analytic Cantor theorem
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shift-compactness
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proper metric
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group-norm
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