Feeding and killing end points in chainable continua

Mapping Chainable Continua onto Dendroids

We prove that every chainable continuum can be mapped into a dendroid such that all point-inverses consist of at most three points. In particular, it follows that there exists a finite-to-one map from a hereditarily indecomposable continuum (the pseudoarc) onto hereditarily decomposable continuum. This answers a question by J. Krasinkiewicz.

The nonexistence of expansive homeomorphisms of chainable 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 6= y, then there is an integer n ∈ Z such that d(f(x), f(y)) > c. In this paper, we prove that if a homeomorphism f : X → X of a continuum X can be lifted to an onto map h : P → P of the pseudoarc P , then f is not expansive. As a corollary, we prove that there are no expansive ho...

Topology Proceedings 7 (1982) pp. 391-393: QUESTIONS ON HOMEOMORPHISM GROUPS OF CHAINABLE AND HOMOGENEOUS CONTINUA

Concerning the Cut Points of Continua*

In this paper propositions will be established concerning the collection of all the cut points of a given planef continuum. It will be shown that there does not exist an uncountable collection of mutually exclusive subcontinua of a given continuum M each of which contains at least one cut point of M. With the aid of this fundamental theorem it is shown, among other things, that the set of all t...

Indecomposable Continua and Misiurewicz Points in Exponential Dynamics

In this paper we describe several new types of invariant sets that appear in the Julia sets of the complex exponential functions Eλ(z) = λe z where λ ∈ C. These invariant sets consist of points that share the same itinerary under iteration of Eλ. Since these exponential functions are 2πi periodic, there are several “natural” ways (described below) to decompose the plane into countably many stri...