A sort of strong completeness property for subsets of a non-Archimedean space is defined. On the subsets which satisfy this property there exists a Vietoris continuous selector. The set of discrete closed subsets of R has a continuous selector when it is equipped with the Vietoris topology induced by the Michael line. Some properties of the tree of a non-Archimedean space are used.
A result about selectors in non-Archimedean spaces
ARTICO, GIULIANO;MARCONI, UMBERTO
2001
Abstract
A sort of strong completeness property for subsets of a non-Archimedean space is defined. On the subsets which satisfy this property there exists a Vietoris continuous selector. The set of discrete closed subsets of R has a continuous selector when it is equipped with the Vietoris topology induced by the Michael line. Some properties of the tree of a non-Archimedean space are used.
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