Uniform normality of topological groups and -groups
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.
When finely continuous functions are of the first class of Baire
Wijsman hyperspaces of non-separable metric spaces
Given a metric space ⟨X,ρ⟩, consider its hyperspace of closed sets CL(X) with the Wijsman topology . It is known that is metrizable if and only if X is separable, and it is an open question by Di Maio and Meccariello whether this is equivalent to being normal. We prove that if the weight of X is a regular uncountable cardinal and X is locally separable, then is not normal. We also solve some questions by Cao, Junnila and Moors regarding isolated points in Wijsman hyperspaces.
-products and selections of set-valued mappings
Every lower semi-continuous closed-and-convex valued mapping , where is a -product of metrizable spaces and is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.
-continuity between two pointwise quasi-uniformity spaces.
Вложения в топологические поля и построение поля, пространство которого не нормально
Действительные функции и пространства, близкие к нормальным
Заметка о перистых пространствах
О правильности близостного произведения правильных пространств
О размерности ird, определенной с помощью ретракций
О совпадении размерностей совершенно нормальных бикомпактов.
Отображения систем открытых множеств