Extensions defined using bornologies

• Caterino, Alessandro ^[1] ; Vipera, M. Cristina ^[1]
  1. [1] Università di Perugia

     Università di Perugia

     Perusa, Italia

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 12, Nº. 2, 2011, págs. 81-94
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Many extensions of a space X such that the remainder Y is closed can be constructed as B-extensions, that is, by defining a topology on the disjoint union X [ Y , provided there exists a map, satisfying some conditions, from a basis of Y into the family of the subsets of X which are “unbounded” with respect to a given bornology in X. We give a first example of a (nonregular) extension with closed remainder which cannot be obtained as B-extension. Extensions with closed discrete remainders and extensions whose remainders are retract are mostly considered. We answer some open questions about separation properties and metrizability of B-extensions.