La categoría-base de los abiertos regulares de un espacio topológico.
La notion de fermé dans un espace de Spanier.
If X is a quasitopological space -Spanier space in this paper-, a topological space q X can be associated to X. A subset F of X is called closed if it is closed in q X. Interesting properties of the closed subspaces of a quasitopological space are examined.
Les espaces topologiques, les espaces de proximité et les espaces uniformes d'un point de vue général
L-guilds and binary L-merotopies.
Local compactness in approach spaces. I.
Local compactness in approach spaces. II.
Locally closed sets and LC-continuous functions.
-generalized closed sets.
Measures of compactness in approach spaces
We investigate whether in the setting of approach spaces there exist measures of relative compactness, (relative) sequential compactness and (relative) countable compactness in the same vein as Kuratowski's measure of compactness. The answer is yes. Not only can we prove that such measures exist, but we can give usable formulas for them and we can prove that they behave nicely with respect to each other in the same way as the classical notions.
Metric-fine uniform frames
A locallic version of Hager’s metric-fine spaces is presented. A general definition of -fineness is given and various special cases are considered, notably all metric frames, complete metric frames. Their interactions with each other, quotients, separability, completion and other topological properties are discussed.
Minimal closed sets and maximal closed sets.
Minimality and prehomogeneity.
Modifications of closure collections
More on sg-compact spaces.
More on -closed sets in topological spaces.
More topological cardinal inequalities
A new topological cardinal invariant is defined; it may be considered as a weaker form of the Lindelöf degree.
N-anti-exchange closure operators
Natural continuity space structures on dual Heyting algebras
N-compact frames
We investigate notions of -compactness for frames. We find that the analogues of equivalent conditions defining -compact spaces are no longer equivalent in the frame context. Indeed, the closed quotients of frame ‘-cubes’ are exactly 0-dimensional Lindelöf frames, whereas those frames which satisfy a property based on the ultrafilter condition for spatial -compactness form a much larger class, and better embody what ‘-compact frames’ should be. This latter property is expressible without reference...
Neighborhood spaces.