Caractérisation des compacts métriques contenant un arc
Caractérisation d'espaces polonais d'après des travaux récents de J. P. R. Christensen et D. Preiss
Cardinal invariants of bitopological spaces
Cardinal reflections and point-character of uniformities – counterexamples
Cardinalities and ranks of -bases in topological spaces
Cardinalities of DCCC normal spaces with a rank 2-diagonal
A topological space has a rank 2-diagonal if there exists a diagonal sequence on of rank , that is, there is a countable family of open covers of such that for each , . We say that a space satisfies the Discrete Countable Chain Condition (DCCC for short) if every discrete family of nonempty open subsets of is countable. We mainly prove that if is a DCCC normal space with a rank 2-diagonal, then the cardinality of is at most . Moreover, we prove that if is a first countable...
Cardinalities of metric completions
Cartesian closed hull for metric spaces
Cartesian closed hull for (quasi-)metric spaces (revisited)
An existing description of the cartesian closed topological hull of , the category of extended pseudo-metric spaces and nonexpansive maps, is simplified, and as a result, this hull is shown to be a special instance of a “family” of cartesian closed topological subconstructs of , the category of extended pseudo-quasi-semi-metric spaces (also known as quasi-distance spaces) and nonexpansive maps. Furthermore, another special instance of this family yields the cartesian closed topological hull of...
Cartesian closed hull of uniform spaces
Cartesian products of -spaces.
Cartesian-closed coreflective subcategories of uniform spaces
Categorial refinements and their relation to reflective subcategories
Categorical aspects of the classical Ascoli theorems
Category bases.
Category measures on Baire spaces.
The purpose of this paper is to give a necessary and sufficient condition to define a category measure on a Baire topological space. In the last section we give some examples of spaces in these conditions.
Category theorems concerning Z-density continuous functions
The ℑ-density topology on ℝ is a refinement of the natural topology. It is a category analogue of the density topology [9, 10]. This paper is concerned with ℑ-density continuous functions, i.e., the real functions that are continuous when the ℑ-densitytopology is used on the domain and the range. It is shown that the family of ordinary continuous functions f: [0,1]→ℝ which have at least one point of ℑ-density continuity is a first category subset of C([0,1])= f: [0,1]→ℝ: f is continuous equipped...
Cauchy completion in category theory
Cauchy nets and open colorings.
Cauchy Sequences in Quasi-Pseudo-Metric Spaces.