Uniformly discrete hit-and-miss hypertopology. A missing link in hypertopologies
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.
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1. Somashekhar Naimpally, 1931–2014
G. Beer, A. Di Concilio, G. Di Maio, S. Naimpally, C.M. Pareek, J.F. Peters
Topology and its Applications vol: 188 first page: 97 year: 2015
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Universitat Politècnica de València
e-ISSN: 1989-4147 https://doi.org/10.4995/agt