Título inglés |
On the three-space problem and the lifting of bounded sets. |
Título español |
El problema de los tres espacios y el levantamiento de conjuntos acotados. |
Autor/es |
Dierolf, Susanne |
Organización |
FB IV - Math. Univ. Trier, Trier, Alemania |
Revista |
0010-0757 |
Publicación |
1993, 44(1-2-3): 81-89, 19 Ref. |
Tipo de documento |
articulo |
Idioma |
Inglés |
Resumen inglés |
We exhibit a general method to show that for several classes of Fréchet spaces the Three-space-problem fails. This method works for instance for the class of distinguished Fréchet spaces, for Fréchet spaces with the density condition and also for dual Fréchet spaces (which gives a negative answer to a question of D. Vogt). An example of a Banach space, which is not a dual Banach space but the strong dual of a DF-space, shows that there are two real different possibilities of defining the notion of a dual Fréchet space. If in a Three-space-problem the corresponding quotient map is assumed to lift bounded sets, we obtain partial positive answers. Finally, we give this property of lifting bounded sets a special treatment. |
Clasificación UNESCO |
120225 |
Palabras clave español |
Problema de tres espacios ; Espacios vectoriales topológicos ; Espacios de Frechet |
Código MathReviews |
MR1280727 |
Código Z-Math |
Zbl 0803.46001 |
Acceso al artículo completo |