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.
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 homology for movable compacta
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.
Cells and cubes in hyperspaces
Cellularity of a space of subgroups of a discrete group
Given a discrete group , we consider the set of all subgroups of endowed with topology of pointwise convergence arising from the standard embedding of into the Cantor cube . We show that the cellularity for every abelian group , and, for every infinite cardinal , we construct a group with .
Chain conditions and products