Countable sums and products of Loeb and selective metric spaces
We investigate the role that weak forms of the axiom of choice play in countable Tychonoff products, as well as countable disjoint unions, of Loeb and selective metric spaces.
Covering dimension modulo a class of spaces
Decomposition spaces and shape in the sense of Fox
Developable and metrizable spaces and problems of Fletcher and Lindgren and Gittings.
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...
Diameters in locales: How bad they can be
Die Hausdorff-Dimension von kartesischen Produkten metrischer Räume.
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...
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
Distances invariantes et L-cliques sur certains demi-groupes finis
Divisible Linearly Ordered Topological Spaces
Dual approach to edge distance between graphs
Eine Bemerkung zu total beschränkten Mengen.
Enlarging the convergence on the real line via metrizable group topologies
Equivalent metrics and the spans of graphs
We present a result which affords the existence of equivalent metrics on a space having distances between certain pairs of points predetermined, with some restrictions. This result is then applied to obtain metric spaces which have interesting properties pertaining to the span, semispan, and symmetric span of metric continua. In particular, we show that no two of these variants of span agree for all simple closed curves or for all simple triods.
Errata to the paper “On paracompact locales and metric locales”
Errata to the paper "Some properties of convex metric spaces" Fundamenta Mathematicae 73 (1972), pp. 193-198
Estimating mathematical information on Graphs: A Scientific Approach