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
Spaces of continuous characteristic functions
We show that if is first-countable, of countable extent, and a subspace of some ordinal, then is Lindelöf.
Spaces of continuous step functions over LOTS
We investigate spaces over LOTS (linearly ordered topological spaces). We find natural necessary conditions for linear Lindelöfness of over LOTS. We also characterize countably compact LOTS whose is linearly Lindelöf for each n. Both the necessary conditions and the characterization are given in terms of the topology of the Dedekind completion of a LOTS.
Spaces whose connected expansion preserve connected subsets
Spaces with Boolean assemblies
Splittability for ordered topological spaces
In quest'articolo dimostriamo come il concetto «spezzabilità», formulato e sviluppato di Arhangel'skii, viene trasferito dallo studio di spazi topologici a quello di spazi topologici parzialmente ordinati. Otteniamo numerosi risultati in forma «se è spezzabile (facendo uso di funzioni appropriatamente scelte) su spazi che hanno una proprietà, allora anche soddisfa la stessa proprietà».
Stationary sets and paracompactness in ordered spaces: a survey
Stationary sets, trees and continuums.
Stone lattices: a topological approach
Subparacompactness in Cartesian products of generalized ordered topological spaces
The covering dimension of product of generalized Sorgenfrey lines
The duality between lattice-ordered monoids and ordered topological spaces.
The -topology on compact spaces
The Gruenhage property, property *, fragmentability, and σ-isolated networks in generalized ordered spaces
We examine the Gruenhage property, property * (introduced by Orihuela, Smith, and Troyanski), fragmentability, and the existence of σ-isolated networks in the context of linearly ordered topological spaces (LOTS), generalized ordered spaces (GO-spaces), and monotonically normal spaces. We show that any monotonically normal space with property * or with a σ-isolated network must be hereditarily paracompact, so that property * and the Gruenhage property are equivalent in monotonically normal spaces....
The ideal and new interval topologies on l-groups
The injective hull and the bc-hull of a topological space.
The Lattice of Kernel Operators and Topological Algebra.