Note on limits of simply continuous and cliquish functions (Q1335490)
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scientific article; zbMATH DE number 650812
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Note on limits of simply continuous and cliquish functions |
scientific article; zbMATH DE number 650812 |
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Note on limits of simply continuous and cliquish functions (English)
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9 October 1994
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Summary: The main result of this paper is that any function \(f\) defined on a perfect Baire space \((X,T)\) with values in a separable metric space \(Y\) is cliquish (has the Baire property) iff it is a uniform (pointwise) limit of sequence \(\{f_ n : n \geq 1\}\) of simply continuous functions. This result is obtained by a change of a topology on \(X\) and showing that a function \(f:(X,T) \to Y\) is cliquish (has the Baire property) iff it is of the Baire class 1 (class 2) with respect to the new topology.
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simple continuity
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cliquishness
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function with the Baire property
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perfect Baire space
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