On decompositions of hereditarily smooth continua
On decompositions of hereditarily unicoherent continua
On decompositions of smooth continua
On decompositions of λ-dendroids
On deductive varieties of locally convex spaces
On dendroids and their end-points and ramification points in the classical sense
On dendroids and their ramification points in the classical sense
On dense subspaces of certain topological spaces
On dense subspaces satisfying stronger separation axioms
We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of -weight less than has a dense completely Hausdorff (and hence Urysohn) subspace. We show that...
On density modulo 1 of some expressions containing algebraic integers
On derivations of quantales
A quantale is a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins. We define the notions of right (left, two) sided derivation and idempotent derivation and investigate the properties of them. It’s well known that quantic nucleus and quantic conucleus play important roles in a quantale. In this paper, the relationships between derivation and quantic nucleus (conucleus) are studied via introducing the concept of pre-derivation.
On descriptive classification of functions
On determining sets for certain generalizations of continuity
On determining sets for the class of somewhat continuous functions
On difficulties in embedding lattice-ordered integral domains in lattice-ordered fields
On dimension and metrization
On dimension of locally pseudocompact groups and their quotients
On Dimensional Functions and Topological Markov Chains.
On dimensional properties of infinite-dimensional spaces
On dimensionally restricted maps
Let f: X → Y be a closed n-dimensional surjective map of metrizable spaces. It is shown that if Y is a C-space, then: (1) the set of all maps g: X → ⁿ with dim(f △ g) = 0 is uniformly dense in C(X,ⁿ); (2) for every 0 ≤ k ≤ n-1 there exists an -subset of X such that and the restriction is (n-k-1)-dimensional. These are extensions of theorems by Pasynkov and Toruńczyk, respectively, obtained for finite-dimensional spaces. A generalization of a result due to Dranishnikov and Uspenskij about...