A~natural strengthening of the completeness hypothesis, called B-completeness, allows us to extend to omega_mu-metric spaces some properties of complete metric spaces which fail to hold if only the completeness condition is assumed. In this way we achieve some results on hyperspace theory, dealing with supercompleteness and with selections of multivalued functions. The notion of B-completeness is investigated and it is proved that quite important classes of omega_mu-metric spaces have this property.
A strong completeness condition in uniform spaces with well ordered bases
MARCONI, UMBERTO;ARTICO, GIULIANO
1999
Abstract
A~natural strengthening of the completeness hypothesis, called B-completeness, allows us to extend to omega_mu-metric spaces some properties of complete metric spaces which fail to hold if only the completeness condition is assumed. In this way we achieve some results on hyperspace theory, dealing with supercompleteness and with selections of multivalued functions. The notion of B-completeness is investigated and it is proved that quite important classes of omega_mu-metric spaces have this property.File in questo prodotto:
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