Topologies generated by closed intervals.
Topologies of Chains.
Topologies sur des espaces ordonnés
Topology and axioms of interpolation in partially ordered spaces.
Topology on ordered fields
An ordered field is a field which has a linear order and the order topology by this order. For a subfield of an ordered field, we give characterizations for to be Dedekind-complete or Archimedean in terms of the order topology and the subspace topology on .
Trees and monotone structures.
T-topologies on a lattice ordered group.
In this paper a characterization of the topologies on a l-group arising from a CTRO (T-topologies) is given. We use it to find conditions under which the Redfield topology comes from a CTRO.
Two theorems concerning BI-quotient maps
Ultraparacompactness in certain Pixley-Roy hyperspaces
Weak orderability of second countable spaces
We demonstrate that a second countable space is weakly orderable if and only if it has a continuous weak selection. This provides a partial positive answer to a question of van Mill and Wattel.
Weak orderability of some spaces which admit a weak selection
We show that if a Hausdorff topological space satisfies one of the following properties: a) has a countable, discrete dense subset and is hereditarily collectionwise Hausdorff; b) has a discrete dense subset and admits a countable base; then the existence of a (continuous) weak selection on implies weak orderability. As a special case of either item a) or b), we obtain the result for every separable metrizable space with a discrete dense subset.
Weak selections and weak orderability of function spaces
It is proved that for a zero-dimensional space , the function space has a Vietoris continuous selection for its hyperspace of at most 2-point sets if and only if is separable. This provides the complete affirmative solution to a question posed by Tamariz-Mascarúa. It is also obtained that for a strongly zero-dimensional metrizable space , the function space is weakly orderable if and only if its hyperspace of at most 2-point sets has a Vietoris continuous selection. This provides a partial...
Weakly smooth dendroids
κ-compactness, extent and the Lindelöf number in LOTS
We study the behaviour of ℵ-compactness, extent and Lindelöf number in lexicographic products of linearly ordered spaces. It is seen, in particular, that for the case that all spaces are bounded all these properties behave very well when taking lexicographic products. We also give characterizations of these notions for generalized ordered spaces.
О бикомпактах, соабсолютных с линейно упорядоченными.
О некоторых видах сходимости по упорядочению и топологиях в частично упорядоченных множествах
О подпространствах -приизведения отрезков
О связи между деревьями Ароншайна и неметризуемыми aleph//0-монолитными линейно упорядоченными бикомпактами, удовлетворяющими первой аксиоме счетности
О топологической полноте булевых алгебр в секвенциальной порядковой топологии.
Одно свойство неприводимых образов экстремально несвязных гиперстоуновых бикомпактов и его приложение к теории полуупорядоченных пространств