On filling an irreducible continuum with the Cartesian product of 1-dimensional continua
On fine shape theory II
On finite sum theorems for transfinite inductive dimensions
We discuss the exactness of estimates in the finite sum theorems for transfinite inductive dimensions trind and trInd. The technique obtained gives an opportunity to repeat and sometimes strengthen some well known results about compacta with trind ≠ trInd. In particular we improve an estimate of the small transfinite inductive dimension of Smirnov’s compacta , given by Luxemburg [Lu2].
On finite-dimensional maps and other maps with "small" fibers
We prove that if f is a k-dimensional map on a compact metrizable space X then there exists a σ-compact (k-1)-dimensional subset A of X such that f|X∖A is 1-dimensional. Equivalently, there exists a map g of X in such that dim(f × g)=1. These are extensions of theorems by Toruńczyk and Pasynkov obtained under the additional assumption that f(X) is finite-dimensional. These results are then extended to maps with fibers restricted to some classes of spaces other than the class of k-dimensional...
On finitely equivalent continua.
On finitely Suslinian continua
On fixed point theorems for multifunctions in dendroids
On f.p.p. and f.*p.p. of some not locally connected continua
On -finitistic spaces and related notions.
On generalizations of dyadic spaces
On generalized homogeneity of locally connected plane continua
The well-known result of S. Mazurkiewicz that the simple closed curve is the only nondegenerate locally connected plane homogeneous continuum is extended to generalized homogeneity with respect to some other classes of mappings. Several open problems in the area are posed.
On generalized ordered spaces [Book]
On H. Priestley's dual of the category of bounded distributive lattices
On hereditarily decomposable hereditarily equivalent non-metric continua
On hereditarily indecomposable compacta
On hereditary interval algebras.
On homogeneous totally disconnected 1-dimensional spaces
The Cantor set and the set of irrational numbers are examples of 0-dimensional, totally disconnected, homogeneous spaces which admit elegant characterizations and which play a crucial role in analysis and dynamical systems. In this paper we will start the study of 1-dimensional, totally disconnected, homogeneous spaces. We will provide a characterization of such spaces and use it to show that many examples of such spaces which exist in the literature in various fields are all homeomorphic. In particular,...
On homotopically regular mappings of manifolds
On indecomposability and composants of chaotic continua
A homeomorphism f:X → X of a compactum X with metric d is expansive if there is c > 0 such that if x,y ∈ X and x ≠ y, then there is an integer n ∈ ℤ such that . A homeomorphism f: X → X is continuum-wise expansive if there is c > 0 such that if A is a nondegenerate subcontinuum of X, then there is an integer n ∈ ℤ such that . Clearly, every expansive homeomorphism is continuum-wise expansive, but the converse assertion is not true. In [6], we defined the notion of chaotic continua of homeomorphisms...
On indecomposable subcontinua of surfaces