-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.