Diffeomorphism groups on noncompact manifolds
Dimension of free L-spaces
Dimension of quasi-metrizable spaces and bicompleteness degree.
Dimension-raising maps in a large scale
Hurewicz's dimension-raising theorem states that dim Y ≤ dim X + n for every n-to-1 map f: X → Y. In this paper we introduce a new notion of finite-to-one like map in a large scale setting. Using this notion we formulate a dimension-raising type theorem for asymptotic dimension and asymptotic Assouad-Nagata dimension. It is also well-known (Hurewicz's finite-to-one mapping theorem) that dim X ≤ n if and only if there exists an (n+1)-to-1 map from a 0-dimensional space onto X. We formulate a finite-to-one...
Direct sums of stratifiable spaces
Disasters in metric topology without choice
We show that it is consistent with ZF that there is a dense-in-itself compact metric space which has the countable chain condition (ccc), but is neither separable nor second countable. It is also shown that has an open dense subspace which is not paracompact and that in ZF the Principle of Dependent Choice, DC, does not imply the disjoint union of metrizable spaces is normal.
Discontinuous groups in some metric and nonmetric spaces
Discrete homotopy theory and critical values of metric spaces
Utilizing the discrete homotopy methods developed for uniform spaces by Berestovskii-Plaut, we define the critical spectrum Cr(X) of a metric space, generalizing to the non-geodesic case the covering spectrum defined by Sormani-Wei and the homotopy critical spectrum defined by Plaut-Wilkins. If X is geodesic, Cr(X) is the same as the homotopy critical spectrum, which differs from the covering spectrum by a factor of 3/2. The latter two spectra are known to be discrete for compact geodesic spaces,...
Distances invariantes et L-cliques sur certains demi-groupes finis
Distinguishable sets
Divisible Linearly Ordered Topological Spaces
Doitchinov's Construct of Supertopological Spaces is Topological
It is shown that the construct of supertopological spaces and continuous maps is topological.
Domain representability of
Let be the space of continuous real-valued functions on X, with the topology of pointwise convergence. We consider the following three properties of a space X: (a) is Scott-domain representable; (b) is domain representable; (c) X is discrete. We show that those three properties are mutually equivalent in any normal T₁-space, and that properties (a) and (c) are equivalent in any completely regular pseudo-normal space. For normal spaces, this generalizes the recent result of Tkachuk that is...
Domain-representable spaces
We study domain-representable spaces, i.e., spaces that can be represented as the space of maximal elements of some continuous directed-complete partial order (= domain) with the Scott topology. We show that the Michael and Sorgenfrey lines are of this type, as is any subspace of any space of ordinals. We show that any completely regular space is a closed subset of some domain-representable space, and that if X is domain-representable, then so is any -subspace of X. It follows that any Čech-complete...
Dual approach to edge distance between graphs
Duality of measure and category in infinite-dimensional separable Hilbert space .
Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals [Book]
Durch Äquivalenzrelationen beschreibbare uniforme Strukturen.
Dynamische Systeme und topologische Aktionen.