We introduce the concept of firm classes of morphisms as basis for the axiomatic study of completions of objects in arbitrary categories. Results on objects injective with respect to given morphism classes are included. In a finitely well-complete category, firm classes are precisely the coessential first factors of morphism factorization structures.
The paper is devoted to the study of the ordered set of all, up to equivalence, -compactifications of an Alexandroff space . The notion of -weight (denoted by ) of an Alexandroff space is introduced and investigated. Using results in ([7]) and ([5]), lattice properties of and are studied, where is the set of all, up to equivalence, -compactifications of for which . A characterization of the families of bounded functions generating an -compactification of is obtained. The notion...
The main purpose of the present paper is to established conditions for a continuous dependence of fixed points of -contractive mappings in uniform spaces. An application to nonlinear functional differential equations of neutral type have been made.
Costruiamo uno spazio nontransitivo analogo al piano di Kofner. Mentre gli argomenti usati per la costruzione del piano di Kofner si fondano su riflessioni geometriche, le nostre prove si basano su idee combinatorie.
Short proofs of the fact that the limit space of a non-gauged approximate system of non-empty compact uniform spaces is non-empty and of two related results are given.
We present the original proof, based on the Doitchinov completion, that a totally bounded quiet quasi-uniformity is a uniformity. The proof was obtained about ten years ago, but never published. In the mean-time several stronger results have been obtained by more direct arguments [8, 9, 10]. In particular it follows from Künzi’s [8] proofs that each totally bounded locally quiet quasi-uniform space is uniform, and recently Déak [10] observed that even each totally bounded Cauchy quasi-uniformity...