Inhomogeneities 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

Chainable Subcontinua

This paper is concerned with conditions under which a metric continuum (a compact connected metric space) contains a nondegenerate chainable continuum. This paper is concerned with conditions under which a metric continuum (a compact connected metric space) contains a non-degenerate chainable continuum. By R.H. Bing’s theorem eleven [2] if a metric continuum X contains a non-degenerate subconti...

Topology Proceedings 42 (2013) pp. 327-340: Concerning Chainability of Inverse Limits on $[0,1]$ with Set-Valued Functions

Suppose that X1, X2, X3, . . . is a sequence of continua and fi : Xi+1 → 2Xi is an upper semi-continuous set-valued function for each positive integer i; let Gn = {x ∈ ∏n+1 i=1 Xi | xi ∈ fi(xi+1) for 1 ≤ i ≤ n}. We show that if Gn is a chainable continuum for each n ∈ N, then the inverse limit lim ←− is chainable. We use this to show that two well-studied examples of inverse limits on [0, 1] wi...