The smallest subring of the ring \(C_ p(C_ p(X))\) containing X\(\cup \{1\}\) is everywhere dense in \(C_ p(C_ p(X))\) (Q578644)
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scientific article; zbMATH DE number 4013509
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The smallest subring of the ring \(C_ p(C_ p(X))\) containing X\(\cup \{1\}\) is everywhere dense in \(C_ p(C_ p(X))\) |
scientific article; zbMATH DE number 4013509 |
Statements
The smallest subring of the ring \(C_ p(C_ p(X))\) containing X\(\cup \{1\}\) is everywhere dense in \(C_ p(C_ p(X))\) (English)
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1987
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A Tikhonov space X is called k-separable if it contains a dense countable union of compact sets. It is shown that if X is k-separable then so is \(C_ p(C_ p(X))\) (the converse is not true). This result follows from the following one: If \(Y\subset X\) then the smallest ring in \(C_ p(C_ p(X))\) containing Y and all constant functions is dense in \(C_ p(C_ p(X))\) iff Y is dense in X.
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k-separable space
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