On topological groups with a first-countable remainder (Q2850647)
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scientific article; zbMATH DE number 6212852
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On topological groups with a first-countable remainder |
scientific article; zbMATH DE number 6212852 |
Statements
27 September 2013
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character
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compactification
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first-countable
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metrizable
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\(\pi\)-base
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remainder
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topological group
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On topological groups with a first-countable remainder (English)
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The authors prove that if a topological group \(G\) is not locally compact and \(bG\setminus G\) is first countable for some compactifiction \(b G\) of the space \(G\), then \(\chi(G)\leq\omega_1\). They also show that this estimation of the character of \(G\) is the best possible, i.e., there exists a non-locally compact topological group \(G\) such that its remainder in some compactification is first countable and \(\chi(G)=\omega_1\).
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