Some examples of irreducibly confluent mappings

On Quasi-ω-Confluent Mappings

Hereditarily Weakly Confluent Mappings onto S

Results are obtained about the existence and behavior of hereditarily weakly confluent maps of continua onto the unit circle S1. A simple and useful necessary and sufficient condition is given for a map of a continuum, X, onto S1 to be hereditarily weakly confluent (HWC). It is shown that when X is arcwise connected, an HWC map of X onto S1 is monotone with arcwise connected fibers. A number of...

Weakly Confluent Mappings and Finitely-generated Cohomology

In this paper we answer a question of Wayne Lewis by proving that if X is a one-dimensional, hereditarily indecomposable continuum and if HX(X) is finitely generated, then C(X), the hyperspace of subcontinua of X, has dimension 2. Let C(A) be the hyperspace of subcontinua of the continuum X with the topology determined by the Hausdorff metric. A classical theorem of J. L. Kelley [4] asserts tha...

Examples of Uniformly Quasiregular Mappings

In this paper we construct examples of uniformly quasiregular (uqr) mappings. These provide counterexamples for a rigidity conjecture in quasiregular dynamics. It states that a closed manifold of dimension at least three, which admits a branched uqr mapping, is quasiconformally equivalent to an ordinary sphere Sn. 1. Statements and results In this paper we construct examples of a certain type o...

Examples of Fixed Point Free Mappings

If X is the dual space of a given Banach space E , X = E*, we say that X has the weak* fixed point property (w*-fpp) if for every nonempty weak* compact (that is, cr(X, E)-co~npact) convex subset C of X and every nonexpansive mapping T : C + C we have Fix(T) # 0. Which subsets of X are weak* compact depends on the choice of pre-dual. Thus, when discussing the w*-fpp it is important that we have...