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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| Format: | Article |
| Language: | English |
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Wiley
1994-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171294000645 |
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| _version_ | 1832558109464199168 |
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| author | Janina Ewert |
| author_facet | Janina Ewert |
| author_sort | Janina Ewert |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7dc8ea7a297d4e07823ef7037338ed04 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1994-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-7dc8ea7a297d4e07823ef7037338ed042025-02-03T01:33:10ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-0117344745010.1155/S0161171294000645Note on limits of simply continuous and cliquish functionsJanina Ewert0Department of Mathematics, Pedagogical University, Arciszewskiego 22, Słupsk 76-200, PolandThe 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.http://dx.doi.org/10.1155/S0161171294000645simply continuitycliquishnessfunction with the Baire propertyfunction of a Baire class α. |
| spellingShingle | Janina Ewert Note on limits of simply continuous and cliquish functions International Journal of Mathematics and Mathematical Sciences simply continuity cliquishness function with the Baire property function of a Baire class α. |
| title | Note on limits of simply continuous and cliquish functions |
| title_full | Note on limits of simply continuous and cliquish functions |
| title_fullStr | Note on limits of simply continuous and cliquish functions |
| title_full_unstemmed | Note on limits of simply continuous and cliquish functions |
| title_short | Note on limits of simply continuous and cliquish functions |
| title_sort | note on limits of simply continuous and cliquish functions |
| topic | simply continuity cliquishness function with the Baire property function of a Baire class α. |
| url | http://dx.doi.org/10.1155/S0161171294000645 |
| work_keys_str_mv | AT janinaewert noteonlimitsofsimplycontinuousandcliquishfunctions |