Compact Resolutions and Analyticity
[EN] We consider the large class (5 of locally convex spaces that includes, among others, the classes of (DF)-spaces and (LF)-spaces. For a space E in class (5 we have characterized that a subspace Y of (E , sigma (E , E ')) , endowed with the induced topology, is analytic if and only if Y...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/219877 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/219877 |
| Access Level: | acceso abierto |
| Palabra clave: | Compact resolution Analytic space Locally convex space Weak metrizability Cp(X)-spaces |
| Sumario: | [EN] We consider the large class (5 of locally convex spaces that includes, among others, the classes of (DF)-spaces and (LF)-spaces. For a space E in class (5 we have characterized that a subspace Y of (E , sigma (E , E ')) , endowed with the induced topology, is analytic if and only if Y has a sigma (E , E ')-compact resolution and is contained in a sigma(E , E ')-separable subset of E. This result is applied to reprove a known important result (due to Cascales and Orihuela) about weak metrizability of weakly compact sets in spaces of class (5. The mentioned characterization follows from the following analogous result: The space C(X) of continuous real -valued functions on a completely regular Hausdorff space X endowed with a topology xi stronger or equal than the pointwise topology tau p of C(X) is analytic iff (C(X) , xi) is separable and is covered by a compact resolution.functions on a completely regular Hausdorff space $X$ endowed with a topology $\xi $ stronger or equal than the pointwise topology $\tau _{p}$ of $C(X)$ is analytic iff $(C(X),\xi )$ is separable and is covered by a compact resolution. |
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