Uniformly discrete hit-and-miss hypertopology. A missing link in hypertopologies

• Di Maio, Giuseppe ^[1] ; Meccariello, Enrico ^[2] ; Naimpally, Somashekhar
  1. [1] Seconda Università degli Studi di Napoli
  2. [2] Università del Sannio
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 7, Nº. 2, 2006, págs. 245-252
• Idioma: inglés
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• Resumen

  • Recently it was shown that the lower Hausdorff metric (uniform) topology is generated by families of uniformly discrete sets as hit sets. This result leads to a new hypertopology which is the join of the above topology and the upper Vietoris topology. This uniformly discrete hit-and-miss hypertopology is coarser than the locally finite hypertopology and finer than both Hausdorff metric (uniform) topology and Vietoris topology. In this paper this new hypertopology is studied. Here is a Hasse diagram in which each arrow goes from a coarser topology to a finer one and equality follows UC or TB as indicated. The diagram clearly shows that the new (underlined) topology provides the missing link.