Comparative smootheology.
A subobjects structure of the category - of -fuzzy sets over a complete -algebra is investigated, where an -fuzzy set is a pair such that is a set and is a special map. Special subobjects (called complete) of an -fuzzy set which can be identified with some characteristic morphisms are then investigated. It is proved that some truth-valued morphisms , are characteristic morphisms of complete subobjects.
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...
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 une catégorie ordonnée régulière dont le groupoïde des éléments inversibles est ordonné semi-régulier. On associe à les catégories -structurées régulières des fusées régulières et des fusées strictes régulières,...
The paper considers a generalization of the standard completion of a partially ordered set through the collection of all its lower sets.