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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/54159 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |