Decisive Convergence Spaces.
Decomposition of topologies on lattices and hyperspaces [Book]
Dedekind-Endlichkeit und Wohlordenbarkeit.
Densely continuous forms, pointwise topology and cardinal functions
We consider the space of densely continuous forms introduced by Hammer and McCoy and investigated also by Holá . We show some additional properties of and investigate the subspace of locally bounded real-valued densely continuous forms equipped with the topology of pointwise convergence . The largest part of the paper is devoted to the study of various cardinal functions for , in particular: character, pseudocharacter, weight, density, cellularity, diagonal degree, -weight, -character,...
Density Character in Topological Groups.
Derived length for arbitrary topological spaces.
Derived-set axioms for topological spaces
Die Limes-Uniformisierbarkeit der Limesräume.
Differentation under the integral sign and holomorphy.
Dimension theory and fuzzy topological 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.
Disconnectednesses and closure operators
Disconnecting Sets and Decomposition Theories
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 subsets in Hausdorff topoligies.
Distinguishing Lindelöfness and inverse Lindelöfness
On a Hausdorff inverse Lindelöf non Lindelöf topology has been constructed.
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.
Double convergence and products of Fréchet spaces
The paper is devoted to convergence of double sequences and its application to products. In a convergence space we recognize three types of double convergences and points, respectively. We give examples and describe their structure and properties. We investigate the relationship between the topological and convergence closure product of two Fréchet spaces. In particular, we give a necessary and sufficient condition for the topological product of two compact Hausdorff Fréchet spaces to be a Fréchet...
Double Sequences and Iterated Limits in Regular Space
First, we define in Mizar [5], the Cartesian product of two filters bases and the Cartesian product of two filters. After comparing the product of two Fréchet filters on ℕ (F1) with the Fréchet filter on ℕ × ℕ (F2), we compare limF₁ and limF₂ for all double sequences in a non empty topological space. Endou, Okazaki and Shidama formalized in [14] the “convergence in Pringsheim’s sense” for double sequence of real numbers. We show some basic correspondences between the p-convergence and the filter...