-spaces and -spaces.
Canonical and op-canonical lax algebras.
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 topological hull of the construct of closure spaces.
Categories of closure spaces and corresponding lattices
Categories of directed spaces
The main goal of the present paper is to unify two commonly used models of directed spaces: d-spaces and streams. To achieve this, we provide certain "goodness" conditions for d-spaces and streams. Then we prove that the categories of good d-spaces and good streams are isomorphic. Next, we prove that the category of good d-spaces is complete, cocomplete, and cartesian closed (assuming we restrict to compactly generated weak Hausdorff spaces). The category of good d-spaces is large enough to contain...
Circle spaces
Closure spaces and characterizations of filters in terms of their Stone images
Fréchet, strongly Fréchet, productively Fréchet, weakly bisequential and bisequential filters (i.e., neighborhood filters in spaces of the same name) are characterized in a unified manner in terms of their images in the Stone space of ultrafilters. These characterizations involve closure structures on the set of ultrafilters. The case of productively Fréchet filters answers a question of S. Dolecki and turns out to be the only one involving a non topological closure structure.
Coherent spaces constructively
Compact unions of closed subsets are closed and compact intersections of open subsets are open
Completions in biaffine sets.
Components and local prehomogeneity.
Concerning a non-realizability of connected compact semi-separated closure operations by set-systems
Continuous Relations.
Convenient categories for topologists
Convergences for the group of real numbers
Convergencia En Relacion.
Derived-set axioms for topological spaces
Disconnectednesses and closure operators
Doitchinov's Construct of Supertopological Spaces is Topological
It is shown that the construct of supertopological spaces and continuous maps is topological.