Approach merotopological spaces and their completion.
Arrows in the “finite product theorem for certain epireflections'” of R. Frič and D. C. Kent
Atoms in the family of coreflective subcategories of uniform spaces
AUnif: A common supercategory of pMET and Unif.
Booleanization
Booleanization of uniform frames
Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and uniform frames arise.
Cantor-connectedness revisited
Following Preuss' general connectedness theory in topological categories, a connectedness concept for approach spaces is introduced, which unifies topological connectedness in the setting of topological spaces, and Cantor-connectedness in the setting of 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 topological hull of the construct of closure spaces.
Cartesian spaces over and locales over
Cartesian-closed coreflective subcategories of uniform spaces
Categorical properties of iterated power.
Categories of topological spaces with sufficiently many sequentially closed spaces
Cauchy Spaces. I. Structure and Uniformization Theorems.
Cauchy Spaces. II. Regular Completions and Compactifications.
Čech complete nearness spaces
We study Čech complete and strongly Čech complete topological spaces, as well as extensions of topological spaces having these properties. Since these two types of completeness are defined by means of covering properties, it is quite natural that they should have a convenient formulation in the setting of nearness spaces and that in that setting these formulations should lead to new insights and results. Our objective here is to give an internal characterization of (and to study) those nearness...
Čech-Stone-like compactifications for general topological spaces
The problem whether every topological space has a compactification such that every continuous mapping from into a compact space has a continuous extension from into is answered in the negative. For some spaces such compactifications exist.
Completely normal locales
Completely regular spaces
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...
Completion and closure