Sober spaces and continuations.
Some problems concerning stability of fixed points
Subspaces in abstract Stone duality.
The compact open topology for semigroups of continuous selfmaps.
The compactificability classes: The behavior at infinity.
The concentration-compactness principle in the calculus of variations. The locally compact case, part 1
The partially pre-ordered set of compactifications of Cp(X, Y)
In the set of compactifications of X we consider the partial pre-order defined by (W, h) ≤X (Z, g) if there is a continuous function f : Z ⇢ W, such that (f ∘ g)(x) = h(x) for every x ∈ X. Two elements (W, h) and (Z, g) of K(X) are equivalent, (W, h) ≡X (Z, g), if there is a homeomorphism h : W ! Z such that (f ∘ g)(x) = h(x) for every x ∈ X. We denote by K(X) the upper semilattice of classes of equivalence of compactifications of X defined by ≤X and ≡X. We analyze in this article K(Cp(X, Y)) where...
The Rothberger property on
A space is said to have the Rothberger property (or simply is Rothberger) if for every sequence of open covers of , there exists for each such that . For any , necessary and sufficient conditions are obtained for to have the Rothberger property when is a Mrówka mad family and, assuming CH (the Continuum Hypothesis), we prove the existence of a maximal almost disjoint family for which the space is Rothberger for all .
The subspace of weak -points of
Let be the subspace of consisting of all weak -points. It is not hard to see that is a pseudocompact space. In this paper we shall prove that this space has stronger pseudocompact properties. Indeed, it is shown that is a -pseudocompact space for all .
The Tensor Product of Continuous Lattices.
The -property in
The -property of a Riesz space (real vector lattice) is: For each sequence of positive elements of , there is a sequence of positive reals, and , with for each . This condition is involved in studies in Riesz spaces of abstract Egoroff-type theorems, and of the countable lifting property. Here, we examine when “” obtains for a Riesz space of continuous real-valued functions . A basic result is: For discrete , has iff the cardinal , Rothberger’s bounding number. Consequences and...
Topological Continuous Convergence.
Topologies between compact and uniform convergence on function spaces.
Two classes of locally compact sober spaces.
Über die Erzeugung von eigentlichen Transformationsgruppen.
Unified spaces and singular sets for mappings of locally compact spaces
Vietoris topology on spaces dominated by second countable ones
For a given space X let C(X) be the family of all compact subsets of X. A space X is dominated by a space M if X has an M-ordered compact cover, this means that there exists a family F = FK : K ∈ C(M) ⊂ C(X) such that ∪ F = X and K ⊂ L implies that FK ⊂ FL for any K;L ∈ C(M). A space X is strongly dominated by a space M if there exists an M-ordered compact cover F such that for any compact K ⊂ X there is F ∈ F such that K ⊂ F . Let K(X) D C(X){Øbe the set of all nonempty compact subsets of a space...
-regular spaces.
О связях между понятиями компактности, линейной компактности и наследственно линейной компактности в топологических кольцах
Об изоморфизме групп когомологий локально компактного пространства и групп расширений модулей