-sets, irresolvable and resolvable spaces
Decompositions of cyclic elements of locally connected continua
Let X denote a locally connected continuum such that cyclic elements have metrizable boundary in X. We study the cyclic elements of X by demonstrating that each such continuum gives rise to an upper semicontinuous decomposition G of X into continua such that X/G is the continuous image of an arc and the cyclic elements of X correspond to the cyclic elements of X/G that are Peano continua.
Decreasing (G) spaces
We consider the class of decreasing (G) spaces introduced by Collins and Roscoe and address the question as to whether it coincides with the class of decreasing (A) spaces. We provide a partial solution to this problem (the answer is yes for homogeneous spaces). We also express decreasing (G) as a monotone normality type condition and explore the preservation of decreasing (G) type properties under closed maps. The corresponding results for decreasing (A) spaces are unknown.
Dedekind-Endlichkeit und Wohlordenbarkeit.
Descent for compact 0-dimensional spaces.
Descriptive compact spaces and renorming
We study the class of descriptive compact spaces, the Banach spaces generated by descriptive compact subsets and their relation to renorming problems.
Diagonal conditions in ordered spaces
For a space X and a regular uncountable cardinal κ ≤ |X| we say that κ ∈ D(X) if for each with |T| = κ, there is an open neighborhood W of Δ(X) such that |T - W| = κ. If then we say that X has a small diagonal, and if every regular uncountable κ ≤ |X| belongs to D(X) then we say that X has an H-diagonal. In this paper we investigate the interplay between D(X) and topological properties of X in the category of generalized ordered spaces. We obtain cardinal invariant theorems and metrization theorems...
Diagonals and discrete subsets of squares
In 2008 Juhász and Szentmiklóssy established that for every compact space there exists a discrete with . We generalize this result in two directions: the first one is to prove that the same holds for any Lindelöf -space and hence is -separable. We give an example of a countably compact space such that is not -separable. On the other hand, we show that for any Lindelöf -space there exists a discrete subset such that ; in particular, the diagonal is a retract of and the projection...
Dichotomies pour les espaces de suites réelles
There is a general conjecture, the dichotomy (C) about Borel equivalence relations E: (i) E is Borel reducible to the equivalence relation where X is a Polish space, and a Polish group acting continuously on X; or (ii) a canonical relation is Borel reducible to E. (C) is only proved for special cases as in [So]. In this paper we make a contribution to the study of (C): a stronger conjecture is true for hereditary subspaces of the Polish space of real sequences, i.e., subspaces such that ...
Dimensions and partitions of unity
Disconnectednesses and closure operators
Disconnectednesses cogenerated by Hausdorff spaces
Disconnecting Sets and Decomposition Theories
Discrete subsets in Hausdorff topoligies.
Distributivity law for the normal triples in the category of compacta and lifting of functors to the categories of algebras
We investigate the triples in the category of compacta whose functorial parts are normal functors in the sense of E.V. Shchepin (normal triples). The problem of lifting of functors to the categories of algebras of the normal triples is considered. The distributive law for normal triples is completely described.
Dualität zwischen Kategorien topologischer Räume und Kategorien von K-Verbänden.
Dugundji spaces and topological groups
Dyadic mappings and dyadic superparacompact topological groups.