Regular inductive limits of K-spaces

• Autores: Thomas E. Gilsdorf
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 42, Fasc. 1, 1991, págs. 45-49
• Idioma: inglés
• Títulos paralelos:
  • Límites inductivos regulares de espacios K
• Enlaces
  • Texto completo
• Resumen

  • A well-known result for bounded sets in inductive limits of locally convex spaces is the following: If each of the constituent spaces En are Fréchet spaces and E is the inductive limit of the spaces En, then each bounded subset of E is bounded in some En iff E is locally complete. Using DeWilde's localization theorem, we show here that the completeness of each En and the local completeness of E may be replaced with the conditions that the spaces En are all webbed K-spaces and E is locally Baire, respectively.

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