Complete permutability of partitions in a set. I
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.
This paper deals with directly indecomposable direct factors of a directed set.
This note establishes that the familiar internal characterizations of the Tychonoff spaces whose rings of continuous real-valued functions are complete, or -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.
The notion of a half lc-group G is a generalization of the notion of a half linearly ordered group. A completion of G by means of Dedekind cuts in linearly ordered sets and applying Świerczkowski's representation theorem of lc-groups is constructed and studied.
The paper considers a generalization of the standard completion of a partially ordered set through the collection of all its lower sets.
In this article, we present a detailed study of the complex calculus of variations introduced in [M. Gondran: Calcul des variations complexe et solutions explicites d’équations d’Hamilton–Jacobi complexes. C.R. Acad. Sci., Paris 2001, t. 332, série I]. This calculus is analogous to the conventional calculus of variations, but is applied here to functions in . It is based on new concepts involving the minimum and convexity of a complex function. Such an approach allows us to propose explicit solutions...