On functionally open and rectangular covers of \(X^ 2\setminus \Delta\) and some topological characteristics of Corson and Eberlein compact sets (Q1107869)
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scientific article; zbMATH DE number 4065904
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On functionally open and rectangular covers of \(X^ 2\setminus \Delta\) and some topological characteristics of Corson and Eberlein compact sets |
scientific article; zbMATH DE number 4065904 |
Statements
On functionally open and rectangular covers of \(X^ 2\setminus \Delta\) and some topological characteristics of Corson and Eberlein compact sets (English)
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1988
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The following theorem is proved: Let X be a compact space. Then the following conditions are equivalent: (1) X is a Corson (Eberlein) compact; (2) \(X^ 2\setminus \Delta\) admits a point-countable (\(\sigma\)- point-finite) functionally open (in \(X^ 2)\) cover; 3) \(X^ 2\setminus \Delta\) admits a point-countable (\(\sigma\)-point-finite) rectangular open cover.
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Corson compact
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Eberlein compact
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point-countable functionally open cover
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point-countable rectangular open cover
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finally compact p-space
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0.8304683566093445
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0.7489866018295288
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0.7428315877914429
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0.741321325302124
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