A hereditary property of HM-spaces.
A nonstandard realization of the J.S. Silva axiomatic theory of distributions
An elementary approach to some applications of nonstandard analysis
An embedding of Schwartz distributions in the algebra of asymptotic functions.
An expression of classical dynamics
Biequivalence vector spaces in the alternative set theory
As a counterpart to classical topological vector spaces in the alternative set theory, biequivalence vector spaces (over the field of all rational numbers) are introduced and their basic properties are listed. A methodological consequence opening a new view towards the relationship between the algebraic and topological dual is quoted. The existence of various types of valuations on a biequivalence vector space inducing its biequivalence is proved. Normability is characterized in terms of total...
Brisure de symétrie spontanée et géométrie du point de vue spectral
Continuous norms on locally convex spaces.
Contribuciones al análisis funcional no-standard.
En este trabajo presentamos aportaciones al tratamiento no-standard del Análisis Funcional en dos direcciones. En la sección 2 la envoltura no-standard de un espacio vectorial topológico, introducida por Luxemburg [7] y por Henson y Moore [2] se aplica al caso de un álgebra topológica. En las secciones 3 y 4 se dan caracterizaciones de elementos accesibles (pre-near-standard) y casi-standard (near-standard) en espacios vectoriales topológicos en términos de una familia filtrante densa de subespacios...
Cyclic monads and their applications.
Cyclically compact operators in Banach spaces.
Dimensional compactness in biequivalence vector spaces
The notion of dimensionally compact class in a biequivalence vector space is introduced. Similarly as the notion of compactness with respect to a -equivalence reflects our nonability to grasp any infinite set under sharp distinction of its elements, the notion of dimensional compactness is related to the fact that we are not able to measure out any infinite set of independent parameters. A fairly natural Galois connection between equivalences on an infinite set and classes of set functions ...
Duaux transfinis.
Expansion of an atomic operator.
Fonctions Généralisées et Analyse Non Standard.
is a Grothendieck space
Indiscernibles and dimensional compactness
This is a contribution to the theory of topological vector spaces within the framework of the alternative set theory. Using indiscernibles we will show that every infinite set in a biequivalence vector space , such that for distinct , contains an infinite independent subset. Consequently, a class is dimensionally compact iff the -equivalence is compact on . This solves a problem from the paper [NPZ 1992] by J. Náter, P. Pulmann and the second author.
Invariant subspaces for polynomially compact almost superdiagonal operators on .
Iteration of ultraproducts of locally convex spaces.