A characterization of the spherically complete normed spaces with a distinguished basis
A characterization of tribes with respect to the Łukasiewicz -norm
We give a complete characterization of tribes with respect to the Łukasiewicz -norm, i. e., of systems of fuzzy sets which are closed with respect to the complement of fuzzy sets and with respect to countably many applications of the Łukasiewicz -norm. We also characterize all operations with respect to which all such tribes are closed. This generalizes the characterizations obtained so far for other fundamental -norms, e. g., for the product -norm.
A corrected correction
A discrete fixed point theorem of Eilenberg as a particular case of the contraction principle.
A method for constructing orthonormal bases for non-archimedean Banach spaces of continuous functions
A non-archimedean analogue of -infrabarreled spaces.
A non-archimedean Dugundji extension theorem
We prove a non-archimedean Dugundji extension theorem for the spaces of continuous bounded functions on an ultranormal space with values in a non-archimedean non-trivially valued complete field . Assuming that is discretely valued and is a closed subspace of we show that there exists an isometric linear extender if is collectionwise normal or is Lindelöf or is separable. We provide also a self contained proof of the known fact that any metrizable compact subspace of an ultraregular...
A scalar field for which -zero has no Hahn-Banach property
About -adic interpolation of continuous and differentiable functions
Absolute values on algebras
Algebraic Weyl system and application
Algèbres -adiques
An application of homological methods to locally convex groups
Analytic functions over valued fields.
Annulation de T-filtres par des fonctions croulantes
Applications of the -adic Nevanlinna theory to functional equations
Let be an algebraically closed field of characteristic zero, complete for an ultrametric absolute value. We apply the -adic Nevanlinna theory to functional equations of the form , where , are meromorphic functions in , or in an “open disk”, satisfying conditions on the order of its zeros and poles. In various cases we show that and must be constant when they are meromorphic in all , or they must be quotients of bounded functions when they are meromorphic in an “open disk”. In particular,...
AQCQ-functional equation in non-Archimedean normed spaces.
Arithmetic aspect of operator algebras
Automorphismes et dérivations de «petites normes» sur un corps value non archimédien