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Complete subobjects of fuzzy sets over M V -algebras

Jiří Močkoř (2004)

Czechoslovak Mathematical Journal

A subobjects structure of the category Ω - of Ω -fuzzy sets over a complete M V -algebra Ω = ( L , , , , ) is investigated, where an Ω -fuzzy set is a pair 𝐀 = ( A , δ ) such that A is a set and δ A × A Ω is a special map. Special subobjects (called complete) of an Ω -fuzzy set 𝐀 which can be identified with some characteristic morphisms 𝐀 Ω * = ( L × L , μ ) are then investigated. It is proved that some truth-valued morphisms ¬ Ω Ω * Ω * , Ω , Ω Ω * × Ω * Ω * are characteristic morphisms of complete subobjects.

Completely regular spaces

H. L. Bentley, Eva Lowen-Colebunders (1991)

Commentationes Mathematicae Universitatis Carolinae

We conduct an investigation of the relationships which exist between various generalizations of complete regularity in the setting of merotopic spaces, with particular attention to filter spaces such as Cauchy spaces and convergence spaces. Our primary contribution consists in the presentation of several counterexamples establishing the divergence of various such generalizations of complete regularity. We give examples of: (1) a contigual zero space which is not weakly regular and is not a Cauchy...

Complétion des catégories ordonnées

Charles Ehresmann (1964)

Annales de l'institut Fourier

Cet article fait suite à trois mémoires parus dans les Annales de l’Institut Fourier (tomes 10, 13 et 14). Son but est d’étendre aux catégories ordonnées les résultats sur les atlas et sur la complétion, précédemment obtenus dans le cas des groupoïdes sous-préinductifs et prélocaux.Soit ( 𝒞 , < ) une catégorie ordonnée régulière dont le groupoïde des éléments inversibles est ordonné semi-régulier. On associe à ( 𝒞 , < ) les catégories Ω ˜ s -structurées régulières des fusées régulières et des fusées strictes régulières,...

Completion of partially ordered sets

Sergey A. Solovyov (2006)

Discussiones Mathematicae - General Algebra and Applications

The paper considers a generalization of the standard completion of a partially ordered set through the collection of all its lower sets.

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