A -continuum is metrizable if and only if it admits a Whitney map for .
A Cantor set in the plane that is not σ-monotone
A metric space (X,d) is monotone if there is a linear order < on X and a constant c such that d(x,y) ≤ cd(x,z) for all x < y < z in X, and σ-monotone if it is a countable union of monotone subspaces. A planar set homeomorphic to the Cantor set that is not σ-monotone is constructed and investigated. It follows that there is a metric on a Cantor set that is not σ-monotone. This answers a question raised by the second author.
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 cubes and spheres [Book]
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 movable compacta.
A characterization of smoothness in dendroids
A characterization of strong inductive dimension
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