Relaciones entre orden, normalidad y completa regularidad.
We study some relations whose compatibility with the topology is equivalent to normality or to complete regularity.
Relative directed homotopy theory of partially ordered spaces.
Remarks on the sobriety of Scott topology and weak topology on posets
We give some necessary and sufficient conditions for the Scott topology on a complete lattice to be sober, and a sufficient condition for the weak topology on a poset to be sober. These generalize the corresponding results in [1], [2] and [4].
Remarks on topologies uniquely determined by their continuous self maps
Selection theorems for partitions of Polish spaces
Selections and approaching points in products
The present paper aims to furnish simple proofs of some recent results about selections on product spaces obtained by García-Ferreira, Miyazaki and Nogura. The topic is discussed in the framework of a result of Katětov about complete normality of products. Also, some applications for products with a countably compact factor are demonstrated as well.
Selections and suborderability
We extend van Mill-Wattel's results and show that each countably compact completely regular space with a continuous selection on couples is suborderable. The result extends also to pseudocompact spaces if they are either scattered, first countable, or connected. An infinite pseudocompact topological group with such a continuous selection is homeomorphic to the Cantor set. A zero-selection is a selection on the hyperspace of closed sets which chooses always an isolated point of a set. Extending Fujii-Nogura...
Selections and weak orderability
We answer a question of van Mill and Wattel by showing that there is a separable locally compact space which admits a continuous weak selection but is not weakly orderable. Furthermore, we show that a separable space which admits a continuous weak selection can be covered by two weakly orderable spaces. Finally, we give a partial answer to a question of Gutev and Nogura by showing that a separable space which admits a continuous weak selection admits a continuous selection for all finite sets.
Semi-ideals in semi-lattices
Semilattice structures on trees.
Separation axioms for partially ordered convergence spaces.
Separation properties of the Wallman ordered compactification.
Simultaneous lattice and topological completion of topological posets
Sobrification of partially ordered sets.
Some approaches to topological spaces.
Some fixed point theorems on ordered metric spaces and application.
Some fixed points theorems in generalized -metric spaces.
Some geometric perspectives in concurrency theory.
Some order theoretic characterizations of the 3-cell
Some properties of cardinal functions, II