Sätze aus der Functionentheorie
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.
Semialgebraic Topology over a Real Closed Field II: Basic Theory of Semialgebraic Spaces.
Semi-confluent and weakly confluent images of tree-like and atriodic continua
Semi-confluent mappings.
Semi-confluent mappings and their invariants
Semigroups in which ... and ... coincide for regular elements.
Semigroups on -spaces
Semigroups whose regular ... -classes form well-ordered chains.
Semigroups whose regular J-classes form finite lattices.
Semigroups with only finitely many regular ... -classes.
Semi-ideals in semi-lattices
Semilattice structures on trees.
Separation axioms for partially ordered convergence spaces.
Separation properties of the Wallman ordered compactification.
Sets of end-points and ramification points in dendroids
Shadowing and expansivity in subspaces
We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain expanding maps have shadowing, and generalize some known results in this area. We also investigate the impact of our theory on maps of the interval.