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Biequivalence vector spaces in the alternative set theory

Miroslav Šmíd, Pavol Zlatoš (1991)

Commentationes Mathematicae Universitatis Carolinae

As a counterpart to classical topological vector spaces in the alternative set theory, biequivalence vector spaces (over the field Q 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...

Contribuciones al análisis funcional no-standard.

José Luis Rubio de Francia (1981)

Revista Matemática Hispanoamericana

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...

Dimensional compactness in biequivalence vector spaces

J. Náter, P. Pulmann, Pavol Zlatoš (1992)

Commentationes Mathematicae Universitatis Carolinae

The notion of dimensionally compact class in a biequivalence vector space is introduced. Similarly as the notion of compactness with respect to a π -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 s and classes of set functions s Q ...

Indiscernibles and dimensional compactness

C. Ward Henson, Pavol Zlatoš (1996)

Commentationes Mathematicae Universitatis Carolinae

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 u S G in a biequivalence vector space W , M , G , such that x - y M for distinct x , y u , contains an infinite independent subset. Consequently, a class X G is dimensionally compact iff the π -equivalence M is compact on X . This solves a problem from the paper [NPZ 1992] by J. Náter, P. Pulmann and the second author.

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