Open Maps between Knaster Continua

Homotopy Classes of Maps between Knaster Continua

For each positive integer n, let gn : I → I be defined by the formula gn (t) = v (nt). Observe that gn stretches n times and then folds the resulting interval [0, n] onto [0, 1]. The map g2 is the very well known “roof-top” map. For any two positive integers m and n, gm ◦ gn = gmn. Consequently, gn and gm commute (see, for example, [8, Proposition 2.2]). Let N = {n1, n2, . . . } be a sequence o...

Exactly two-to-one maps from continua onto some tree-like continua

It is known that no dendrite (Gottschalk 1947) and no hereditarily indecomposable tree-like continuum (J. Heath 1991) can be the image of a continuum under an exactly 2-to-1 (continuous) map. This paper enlarges the class of tree-like continua satisfying this property, namely to include those tree-like continua whose nondegenerate proper subcontinua are arcs. This includes all Knaster continua ...

Homotopy and Dynamics for Homeomorphisms of Solenoids and Knaster Continua

We describe homotopy classes of self-homeomorphisms of solenoids and Knaster continua. In particular, we demonstrate that homeomorphisms within one homotopy class have the same (explicitly given) topological en-tropy and that they are actually semi-conjugeted to an algebraic homeomor-phism in the case when the entropy is positive.

The Lattice of Knaster Continua

Reduction of Open Mappings

In 1936 G. T. Whyburn [8] defined an irreducible mapping to be a mapping/, of a compact metric continuum A onto B, such that no proper sub-continuum of A maps onto B under/. Similarly, assuming A to be only compact and metric, he defined / to be strongly irreducible provided that no closed proper subset of A maps onto B. J. Rozanska [7] independently defined this second type of mapping in 1937....