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The order topology for function lattices and realcompactness.

Feldman, W.A., Porter, J.F. (1981)

International Journal of Mathematics and Mathematical Sciences

The positive cone of a Banach lattice. Coincidence of topologies and metrizability

Zbigniew Lipecki (2023)

Commentationes Mathematicae Universitatis Carolinae

Let $X$ be a Banach lattice, and denote by $X_{+}$ its positive cone. The weak topology on $X_{+}$ is metrizable if and only if it coincides with the strong topology if and only if $X$ is Banach-lattice isomorphic to $l^{1} (Γ)$ for a set $Γ$ . The weak $^{*}$ topology on $X_{+}^{*}$ is metrizable if and only if $X$ is Banach-lattice isomorphic to a $C (K)$ -space, where $K$ is a metrizable compact space.

Théorèmes de factorisation dans les espaces réticules

J. L. Krivine (1973/1974)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Theorems of the Stone-Weierstrass type for lattices of uniformly continuous functions.

Л.Н. Мохова (1981)

Sibirskij matematiceskij zurnal

Une classe d'espaces de Banach réticulés.

Alain Goullet de Rugy (1975)

Mathematische Zeitschrift

Uniform approximation theorems for real-valued continuous functions.

M. Isabel Garrido, Francisco Montalvo (1991)

Extracta Mathematicae

For a completely regular space X, C(X) and C*(X) denote, respectively, the algebra of all real-valued continuous functions and bounded real-valued continuous functions over X. When X is not a pseudocompact space, i.e., if C*(X) ≠ C(X), theorems about uniform density for subsets of C*(X) are not directly translatable to C(X). In [1], Anderson gives a sufficient condition in order for certain rings of C(X) to be uniformly dense, but this condition is not necessary.In this paper we study the uniform...