Homotopy Classes of Maps between 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.

Open Maps between Knaster Continua

We i n vestigate the set of open maps from one Knaster continuum to another. A structure theorem for the semigroup of open induced maps on a Knaster continuum is obtained. Homeomorphisms w h i c h are not induced are constructed, and it is shown that the induced open maps are dense in the space of open maps between two Knaster continua. Results about the structure of the semigroup of open maps ...

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 ...

Real algebraic morphisms represent few homotopy classes

We study the problem of representing homotopy classes of maps between real algebraic varieties of regular maps.

The Lattice of Knaster Continua