On span and 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...

Span, Chainability and the Continua H

We show that the continua Iu and H * are non-chainable and have span nonzero. Under CH this can be strengthened to surjective symmetric span nonzero. We discuss the logical consequences of this.

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

A Non-chainable Plane Continuum with Span Zero

A plane continuum is constructed which has span zero but is not chainable.