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A subobjects structure of the category $Ω$ - of $Ω$ -fuzzy sets over a complete $M V$ -algebra $Ω = (L, \land, \lor, \otimes, \to)$ is investigated, where an $Ω$ -fuzzy set is a pair $𝐀 = (A, δ)$ such that $A$ is a set and $δ A \times A \to Ω$ is a special map. Special subobjects (called complete) of an $Ω$ -fuzzy set $𝐀$ which can be identified with some characteristic morphisms $𝐀 \to Ω^{*} = (L \times L, μ)$ are then investigated. It is proved that some truth-valued morphisms $\neg_{Ω} Ω^{*} \to Ω^{*}, \cap_{Ω}$ , $\cup_{Ω} Ω^{*} \times Ω^{*} \to Ω^{*}$ are characteristic morphisms of complete subobjects.

Completely distributive latices

M. Lambrou (1983)

Fundamenta Mathematicae

Completely meet-irreducible tolerances in distributive Noetherian lattices

Josef Niederle (1989)

Czechoslovak Mathematical Journal

Completely normal locales

Bohumil Šmarda (1990)

Acta Universitatis Carolinae. Mathematica et Physica

Completely subdirect products of directed sets

Ján Jakubík (2002)

Mathematica Bohemica

This paper deals with directly indecomposable direct factors of a directed set.

Completeness and continuity of lattice-seminorms

Wilhelm, M. (1977)

Abstracta. 5th Winter School on Abstract Analysis

Completeness and modular cross-symmetry in normed linear spaces

Jan Hamhalter (1992)

Czechoslovak Mathematical Journal

Completeness in semi-local ideal lattices

Johnny A. Johnson (1977)

Czechoslovak Mathematical Journal

Completeness properties of function rings in pointfree topology

Bernhard Banaschewski, Sung Sa Hong (2003)

Commentationes Mathematicae Universitatis Carolinae

This note establishes that the familiar internal characterizations of the Tychonoff spaces whose rings of continuous real-valued functions are complete, or $σ$ -complete, as lattice ordered rings already hold in the larger setting of pointfree topology. In addition, we prove the corresponding results for rings of integer-valued functions.

Completion of a class of topological semilattices, applications. (Complétion d'une classe de demi-treillis topologiques, applications.)

Grenier, Jean-Pierre (1996)

Bulletin of the Belgian Mathematical Society - Simon Stevin

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