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Let $M (X, 𝒜)$ ( $M^{*} (X, 𝒜)$ ) be the $f$ -ring of all (bounded) real-measurable functions on a $T$ -measurable space $(X, 𝒜)$ , let $M_{K} (X, 𝒜)$ be the family of all $f \in M (X, 𝒜)$ such that $coz (f)$ is compact, and let $M_{\infty} (X, 𝒜)$ be all $f \in M (X, 𝒜)$ that ${x \in X : | f (x) | \geq \frac{1}{n}}$ is compact for any $n \in ℕ$ . We introduce realcompact subrings of $M (X, 𝒜)$ , we show that $M^{*} (X, 𝒜)$ is a realcompact subring of $M (X, 𝒜)$ , and also $M (X, 𝒜)$ is a realcompact if and only if $(X, 𝒜)$ is a compact measurable space. For every nonzero real Riesz map $ϕ : M (X, 𝒜) \to ℝ$ , we prove that there is an element $x_{0} \in X$ such that $ϕ (f) = f (x_{0})$ for every $f \in M (X, 𝒜)$ if $(X, 𝒜)$ is a compact measurable space. We confirm...

Some remarks on ordered fields

Masayoshi Nagata (1974/1975)

Séminaire Dubreil. Algèbre et théorie des nombres

Some results on the degree of imperfection of complete valued fields.

Gervasio G. Bastos (1978)

Manuscripta mathematica

Spaces of orderings of fields under finite extensions.

Claus Scheiderer (1991)

Manuscripta mathematica

Spécialisation dans les disques singuliers réguliers

Yves André (1985/1986)

Groupe de travail d'analyse ultramétrique

Spectre maximal d'une algèbre de Krasner

Alain Escassut (1973/1974)

Groupe de travail d'analyse ultramétrique

Spectre maximal d'une algèbre de Krasner

Alain Escassut (1978)

Colloquium Mathematicae

Spectres d’algèbres de Banach $p$ -adiques

Alain Escassut (1975/1976)

Groupe de travail d'analyse ultramétrique

Spherical completeness with infinitesimals.

José Manuel Bayod (1982)

Revista Matemática Hispanoamericana

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...

Strict topologies in non-archimedean function spaces.

Katsaras, A.K. (1984)

International Journal of Mathematics and Mathematical Sciences

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