Direct limits of Hausdorff spaces
Direct limits of topological spaces and groups
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.
Disconnected bounded manifolds in Euclidean spaces
Disconnectedness properties of hyperspaces
Let be a Hausdorff space and let be one of the hyperspaces , , or ( a positive integer) with the Vietoris topology. We study the following disconnectedness properties for : extremal disconnectedness, being a -space, -space or weak -space and hereditary disconnectedness. Our main result states: if is Hausdorff and is a closed subset such that (a) both and are totally disconnected, (b) the quotient is hereditarily disconnected, then is hereditarily disconnected. We also...
Disconnectednesses and closure operators
Disconnectednesses cogenerated by Hausdorff spaces
Disconnecting Sets and Decomposition Theories
Discontinuity points of exactly -to-one functions
Discontinuous groups in some metric and nonmetric spaces
Discrete and continuous flows of characteristic
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,...
Discrete n-tuples in Hausdorff spaces
We investigate the following three questions: Let n ∈ ℕ. For which Hausdorff spaces X is it true that whenever Γ is an arbitrary (respectively finite-to-one, respectively injective) function from ℕⁿ to X, there must exist an infinite subset M of ℕ such that Γ[Mⁿ] is discrete? Of course, if n = 1 the answer to all three questions is "all of them". For n ≥ 2 the answers to the second and third questions are the same; in the case n = 2 that answer is "those for which there are only finitely many points...
Discrete orbits in βN-N
Discrete subsets in Hausdorff topoligies.
Distances invariantes et L-cliques sur certains demi-groupes finis
Distinguishable sets
Distinguished boundary sets in the theory of functions of two complex variables
Distinguished subclasses of Čech-analytic spaces