Lebesgue Measurability of Separately Continuous Functions and Separability
A connection between the separability and the countable chain condition of spaces with L-property (a topological space X has L-property if for every topological space Y, separately continuous function f:X×Y→ℝ and open set I⊆ℝ, the set f−1(I) is an Fσ-set) is studied. We show that every completely re...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/54159 |
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| author | V. V. Mykhaylyuk |
| author_facet | V. V. Mykhaylyuk |
| author_sort | V. V. Mykhaylyuk |
| collection | DOAJ |
| description | A connection between the separability and the countable chain condition of spaces with L-property (a topological space X has L-property if for every topological space Y, separately continuous function f:X×Y→ℝ and open set I⊆ℝ, the set f−1(I) is an Fσ-set) is studied. We show that every completely
regular Baire space with the L-property and the countable chain condition is separable and constructs a nonseparable completely regular space with the L-property and the countable chain condition. This gives a negative answer to a question of M. Burke. |
| format | Article |
| id | doaj-art-8ba04952434e4ec486740b4bfb95b0d1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8ba04952434e4ec486740b4bfb95b0d12025-02-03T05:44:22ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/5415954159Lebesgue Measurability of Separately Continuous Functions and SeparabilityV. V. Mykhaylyuk0Department of Mathematical Analysis, Chernivtsi National University, Kotsjubyns'koho 2, Chernivtsi 58012, UkraineA connection between the separability and the countable chain condition of spaces with L-property (a topological space X has L-property if for every topological space Y, separately continuous function f:X×Y→ℝ and open set I⊆ℝ, the set f−1(I) is an Fσ-set) is studied. We show that every completely regular Baire space with the L-property and the countable chain condition is separable and constructs a nonseparable completely regular space with the L-property and the countable chain condition. This gives a negative answer to a question of M. Burke.http://dx.doi.org/10.1155/2007/54159 |
| spellingShingle | V. V. Mykhaylyuk Lebesgue Measurability of Separately Continuous Functions and Separability International Journal of Mathematics and Mathematical Sciences |
| title | Lebesgue Measurability of Separately Continuous Functions and Separability |
| title_full | Lebesgue Measurability of Separately Continuous Functions and Separability |
| title_fullStr | Lebesgue Measurability of Separately Continuous Functions and Separability |
| title_full_unstemmed | Lebesgue Measurability of Separately Continuous Functions and Separability |
| title_short | Lebesgue Measurability of Separately Continuous Functions and Separability |
| title_sort | lebesgue measurability of separately continuous functions and separability |
| url | http://dx.doi.org/10.1155/2007/54159 |
| work_keys_str_mv | AT vvmykhaylyuk lebesguemeasurabilityofseparatelycontinuousfunctionsandseparability |