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
Some properties of uniform ordered spaces
Some questions of Arhangel'skii on rotoids
A rotoid is a space X with a special point e ∈ X and a homeomorphism F: X² → X² having F(x,x) = (x,e) and F(e,x) = (e,x) for every x ∈ X. If any point of X can be used as the point e, then X is called a strong rotoid. We study some general properties of rotoids and prove that the Sorgenfrey line is a strong rotoid, thereby answering several questions posed by A. V. Arhangel'skii, and we pose further questions.
Some results and problems about weakly pseudocompact spaces
A space is truly weakly pseudocompact if is either weakly pseudocompact or Lindelöf locally compact. We prove: (1) every locally weakly pseudocompact space is truly weakly pseudocompact if it is either a generalized linearly ordered space, or a proto-metrizable zero-dimensional space with for every ; (2) every locally bounded space is truly weakly pseudocompact; (3) for , the -Lindelöfication of a discrete space of cardinality is weakly pseudocompact if .
Some results on dimension theory: Universal spaces