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Well-posedness, bornologies, and the structure of metric spaces

  • Beer, Gerald [1] ; Segura, Manuel [1] Árbol académico
    1. [1] California State University Los Angeles

      California State University Los Angeles

      Estados Unidos

  • Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 10, Nº. 1, 2009, págs. 131-157
  • Idioma: inglés
  • DOI: 10.4995/agt.2009.1793
  • Enlaces
  • Resumen

    • Given a continuous nonnegative functional λ that makes sense defined on an arbitrary metric space (X, d), one may consider those spaces in which each sequence (xn) for which lim n→∞λ(xn) = 0 clusters. The compact metric spaces, the complete metric spaces, the cofinally complete metric spaces, and the UC-spaces all arise in this way. Starting with a general continuous nonnegative functional λ defined on (X, d), we study the bornology Bλ of all subsets A of X on which limn→∞λ(an) = 0 ⇒ (an) clusters, treating the possibility X ∈ Bλ as a special case. We characterize those bornologies that can be expressed as Bλ  for some λ, as well as those that can be so induced by a uniformly continuous λ.

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