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A categorical concept of completion of objects

Guillaume C. L. Brümmer, Eraldo Giuli (1992)

Commentationes Mathematicae Universitatis Carolinae

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.

A -compactifications and A -weight of Alexandroff spaces

A. Caterino, G. Dimov, M. C. Vipera (2002)

Bollettino dell'Unione Matematica Italiana

The paper is devoted to the study of the ordered set A K X , α of all, up to equivalence, A -compactifications of an Alexandroff space X , α . The notion of A -weight (denoted by a w X , α ) of an Alexandroff space X , α is introduced and investigated. Using results in ([7]) and ([5]), lattice properties of A K X , α and A K α w X , α are studied, where A K α w X , α is the set of all, up to equivalence, A -compactifications Y of X , α for which w Y = a w X , α . A characterization of the families of bounded functions generating an A -compactification of X , α is obtained. The notion...

A nontransitive space based on combinatorics

Hans-Peter A. Künzi, Stephen Watson (1999)

Bollettino dell'Unione Matematica Italiana

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.

A Note on Totally Bounded Quasi-Uniformities

Fletcher, P., Hunsaker, W. (1998)

Serdica Mathematical Journal

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...

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