Terminal continua and the homogeneity
The classification of circle-like continua that admit expansive homeomorphisms
A homeomorphism h: X → X of a compactum X is expansive provided that for some fixed c > 0 and every x, y ∈ X (x ≠ y) there exists an integer n, dependent only on x and y, such that d(hⁿ(x),hⁿ(y)) > c. It is shown that if X is a solenoid that admits an expansive homeomorphism, then X is homeomorphic to a regular solenoid. It can then be concluded that a circle-like continuum admits an expansive homeomorphism if and only if it is homeomorphic to a regular solenoid.
The existence of local homeomorphisms of degree on local dendrites
In this paper we characterize local dendrites which are the images of themselves under local homeomorphisms of degree for each positive integer .
The fixed point property for set-valued mappings
The fixed point property for some cartesian products
It is proved that the cylinder X × I over a planar λ-dendroid X has the fixed point property. This is a partial solution of two problems posed by R. H. Bing (cf. [1], Questions 9 and 10).
The fixed-point property for deformations of tree-like continua
Let f be a map of a tree-like continuum M that sends each arc-component of M into itself. We prove that f has a fixed point. Hence every tree-like continuum has the fixed-point property for deformations (maps that are homotopic to the identity). This result answers a question of Bellamy. Our proof resembles an old argument of Brouwer involving uncountably many tangent curves. The curves used by Brouwer were originally defined by Peano. In place of these curves, we use rays that were originally defined...
The Freudenthal space for approximate systems of compacta and some applications.
In this paper we define a space σ(X) for approximate systems of compact spaces. The construction is due to H. Freudenthal for usual inverse sequences [4, p. 153–156]. We establish the following properties of this space: (1) The space σ(X) is a paracompact space, (2) Moreover, if X is an approximate sequence of compact (metric) spaces, then σ(X) is a compact (metric) space (Lemma 2.4). We give the following applications of the space σ(X): (3) If X is an approximate system of continua, then X = limX...
The generalized Schoenflies theorem for absolute suspensions
The aim of this paper is to prove the generalized Schoenflies theorem for the class of absolute suspensions. The question whether the finite-dimensional absolute suspensions are homeomorphic to spheres remains open. Partial solution to this question was obtained in [Sz] and [Mi]. Morton Brown gave in [Br] an ingenious proof of the generalized Schoenflies theorem. Careful analysis of his proof reveals that modulo some technical adjustments a similar argument gives an analogous result for the class...
The hereditary classes of mappings
The irreducibility of continua which are the inverse limit of a collection of Hausdorff arcs
The Jordan Curve Theorem Revisited.
The lifting property for classes of mappings.
The metric confluent images of half-lines and lines
The monomorphism semigroup of S(X).
The nonexistence of expansive homeomorphisms of dendroids
The one-point countable compactification of curve spaces and arc spaces
The Peano curves as limit of α-dense curves.
En este artículo presentamos una caracterización de las curvas de Peano como límite uniforme de sucesiones de curvas α-densas en el compacto que es llenado por la curva de Peano. Estas curvas α-densas deben tener densidades tendiendo a cero y sus funciones coordenadas deben de ser de variación tendiendo a infinito cuando α tiende a cero.
The pseudo-arc as an inverse limit with simple bonding maps
The set function T and homotopies
The set functions 𝓣 and 𝒦 and irreducible continua
We study the set functions 𝓣 and 𝒦 on irreducible continua. We present several properties of these functions when defined on irreducible continua. In particular, we characterize the class of irreducible continua for which these functions are continuous. We also characterize the class of 𝒦-symmetric irreducible continua.