Note on limits of simply continuous and cliquish functions
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 {fn:n≥1} of simply continuous functions. This result is obtained by a change of...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1994-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171294000645 |
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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 {fn:n≥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)→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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| ISSN: | 0161-1712 1687-0425 |