Sobrification of partially ordered sets.
Solution to a compactification problem of Sklyarenko
Some applications of minimal open sets.
Some applications of non-standard analysis to proximity spaces
Some applications of the point-open subbase game
Given a subbase of a space , the game is defined for two players and who respectively pick, at the -th move, a point and a set such that . The game stops after the moves have been made and the player wins if ; otherwise is the winner. Since is an evident modification of the well-known point-open game , the primary line of research is to describe the relationship between and for a given subbase . It turns out that, for any subbase , the player has a winning strategy...
Some applications of tiny sequences
Some Baire category type theorems for
Some cardinal generalizations of pseudocompactness
Some characterization of c-paracompact and c-collectionwise normal spaces by continuous selections (II).
Some characterizations of bitopological connectivity properties
Some characterizations of c-paracompact and c-collectionwise normal spaces by continuous selections (I).
In this note we characterize the c-paracompact and c-collectionwise normal spaces in terms of continuous selections. We include the usual techniques with the required modifications by the cardinality.
Some characterizations of paracompactness in k-spaces
Some classes of countably compact spaces
Some compactifications of a semitopological semigroup.
Some continuous separation axioms
Some counterexamples and properties on generalizations of Lindelöf spaces.
Some cover properties of nonseparable metric spaces
Some covering spaces and types of compactness.
Some examples in the dimension theory of Tychonoff spaces
Some examples related to colorings
We complement the literature by proving that for a fixed-point free map the statements (1) admits a finite functionally closed cover with for all (i.e., a coloring) and (2) is fixed-point free are equivalent. When functionally closed is weakened to closed, we show that normality is sufficient to prove equivalence, and give an example to show it cannot be omitted. We also show that a theorem due to van Mill is sharp: for every we construct a strongly zero-dimensional Tychonov space...