A characterization of the arc by means of the C-index of itssemigroup.
A characterization of unicoherence in terms of separating open sets
A class of continua that are not attractors of any IFS
This paper presents a sufficient condition for a continuum in ℝn to be embeddable in ℝn in such a way that its image is not an attractor of any iterated function system. An example of a continuum in ℝ2 that is not an attractor of any weak iterated function system is also given.
A class of infinite-dimensional spaces. Part I: Dimension theory and Alexandrof's problem
A class of infinite-dimensional spaces. Part II: An Extension Theorem and the theory of retracts
A class of spaces that admit no sensitive commutative group actions
We show that a metric space X admits no sensitive commutative group action if it satisfies the following two conditions: (1) X has property S, that is, for each ε > 0 there exists a cover of X which consists of finitely many connected sets with diameter less than ε; (2) X contains a free n-network, that is, there exists a nonempty open set W in X having no isolated point and n ∈ ℕ such that, for any nonempty open set U ⊂ W, there is a nonempty connected open set V ⊂ U such that the boundary ...
A class α and locally connected continua which can be ε-mapped onto a surface
A classification of continua and weakly confluent mappings
A classification of continua by certain cutting properties
A classification of inverse limit spaces of tent maps with periodic critical points
We work within the one-parameter family of symmetric tent maps, where the slope is the parameter. Given two such tent maps , with periodic critical points, we show that the inverse limit spaces and are not homeomorphic when a ≠ b. To obtain our result, we define topological substructures of a composant, called “wrapping points” and “gaps”, and identify properties of these substructures preserved under a homeomorphism.
A collection of dendroids.
A condition equivalent to covering dimension for normal spaces
A condition under which 2-homogeneity and representability are the same in continua
A connected subset of the plane
A connection between multiplication in C(X) and the dimension of X
Let X be a compact Hausdorff topological space. We show that multiplication in the algebra C(X) is open iff dim X < 1. On the other hand, the existence of non-empty open sets U,V ⊂ C(X) satisfying Int(U· V) = ∅ is equivalent to dim X > 1. The preimage of every set of the first category in C(X) under the multiplication map is of the first category in C(X) × C(X) iff dim X ≤ 1.
A construction of noncontractible simply connected cell-like two-dimensional Peano continua
Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts from a noncontractible n-dimensional Peano continuum for any n > 0, then our construction yields a simply connected noncontractible (n + 1)-dimensional cell-like Peano continuum. In particular, starting from the circle 𝕊¹,...
A constructive proof of the Tychonoff's theorem for locales
A continuum without the fixed point property which is quasihomeomorphic with an AR-set
A continuum such that is not continuously homogeneous
A metric continuum is said to be continuously homogeneous provided that for every two points there exists a continuous surjective function such that . Answering a question by W.J. Charatonik and Z. Garncarek, in this paper we show a continuum such that the hyperspace of subcontinua of , , is not continuously homogeneous.
A correction to my paper:"Some topological extensions of plane geometry"