On continua which resemble simple closed curves
On contractible dendroids
On contractible fans
On convex metric spaces II
On countable connected Hausdorff spaces in which the intersection of every pair of connected subsets is connected.
On countable dense and strong n-homogeneity
We prove that if a space X is countable dense homogeneous and no set of size n-1 separates it, then X is strongly n-homogeneous. Our main result is the construction of an example of a Polish space X that is strongly n-homogeneous for every n, but not countable dense homogeneous.
On -property of strong spaces
It is shown that every strong space is a -space. In particular, it follows that every paracompact space is a -space.
On decomposition of projections of finite order
On decompositions of continua
On decompositions of Hausdorff continua [Book]
On decompositions of hereditarily smooth continua
On decompositions of hereditarily unicoherent continua
On decompositions of smooth continua
On decompositions of λ-dendroids
On dendroids and their end-points and ramification points in the classical sense
On dendroids and their ramification points in the classical sense
On dimension of locally pseudocompact groups and their quotients
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...
On Dimensionsgrad, resolutions, and chainable continua
For each natural number n ≥ 1 and each pair of ordinals α,β with n ≤ α ≤ β ≤ ω(⁺), where ω(⁺) is the first ordinal of cardinality ⁺, we construct a continuum such that (a) ; (b) ; (c) ; (d) if β < ω(⁺), then is separable and first countable; (e) if n = 1, then can be made chainable or hereditarily decomposable; (f) if α = β < ω(⁺), then can be made hereditarily indecomposable; (g) if n = 1 and α = β < ω(⁺), then can be made chainable and hereditarily indecomposable. In particular,...
On Eberlein compactifications of metrizable spaces
We prove that, for every finite-dimensional metrizable space, there exists a compactification that is Eberlein compact and preserves both the covering dimension and weight.