Schnitt und Verbindung in projektiven Hjelmsleveschen Räumen.
Let () be the -ring of all (bounded) real-measurable functions on a -measurable space , let be the family of all such that is compact, and let be all that is compact for any . We introduce realcompact subrings of , we show that is a realcompact subring of , and also is a realcompact if and only if is a compact measurable space. For every nonzero real Riesz map , we prove that there is an element such that for every if is a compact measurable space. We confirm...
In the theory of nonarchimedean normed spaces over valued fields other than R or C, the property of spherical completeness is of utmost importance in several contexts, and it appears to play the role conventional completeness does in some topics of classical functional analysis. In this note we give various characterizations of spherical completeness for general ultrametric spaces, related to but different from the notions of pseudo-convergent sequence and pseudo-limit introduced by Ostrowski in...