A -continuum is metrizable if and only if it admits a Whitney map for .
A Cech-Hurewicz Isomorphism Theorem for Movable Metric Compacta.
A chainable continuum not homeomorphic to an inverse limit on [0, 1] with only one bonding map
A characterization of dendroids by the n-connectedness of the Whitney levels
Let X be a continuum. Let C(X) denote the hyperspace of all subcontinua of X. In this paper we prove that the following assertions are equivalent: (a) X is a dendroid, (b) each positive Whitney level in C(X) is 2-connected, and (c) each positive Whitney level in C(X) is ∞-connected (n-connected for each n ≥ 0).
A characterization of finitely irreducible continua
A characterization of hereditarily decomposable snake-like continua
A characterization of local connectedness for generalized continua
A characterization of locally connected continua which are quasi-embeddable into
A characterization of locally connectedness by means of the set function T
A characterization of smoothness in dendroids
A characterization of the arc by means of the C-index of itssemigroup.
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 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 under which 2-homogeneity and representability are the same in continua
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,...