Boolean semigroup rings and exponentials of compact zero-dimensional spaces
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.
Borsuk's Theory of Shape and Cech Homotopy.
Boundedness in topological spaces
Bourbaki's Fixpoint Lemma reconsidered
A constructively valid counterpart to Bourbaki’s Fixpoint Lemma for chain-complete partially ordered sets is presented to obtain a condition for one closure system in a complete lattice to be stable under another closure operator of . This is then used to deal with coproducts and other aspects of frames.
Caliber (, ω) is not productive
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.
Cardinal functions on hyperspaces
Cardinal invariants of paratopological groups
We show that a regular totally ω-narrow paratopological group G has countable index of regularity, i.e., for every neighborhood U of the identity e of G, we can find a neighborhood V of e and a countable family of neighborhoods of e in G such that ∩W∈γ VW−1⊆ U. We prove that every regular (Hausdorff) totally !-narrow paratopological group is completely regular (functionally Hausdorff). We show that the index of regularity of a regular paratopological group is less than or equal to the weak Lindelöf...
Cardinal reflections and point-character of uniformities – counterexamples
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 products of -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.