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A branchpoint of a compactum $ X$. A surjective map $ f:X \to Y$ if each branchpoint in $ Y$. If every map in a class $ \mathcal{F}$ $ \mathcal{C}$ $ \mathcal{F}$ . According to Whyburn's classical theorem on the lifting of dendrites, the branchpoint covering property holds for light open maps on arbitrary compacta. In this paper it is shown that the branchpoint covering property holds for (1) light confluent maps on arbitrary compacta, (2) confluent maps on hereditarily arcwise connected compacta, and (3) weakly confluent maps on hereditarily locally connected continua having closed sets of branchpoints. It follows that the weakly confluent image of a graph is a graph.

Let X be a uniquely arcwise-connected continuum and $ f:X \to X$f has a fixed point.

This paper is concerned with the fixed point sets of certain collections of homeomorphisms on a tree-like continuum. Extending a theorem of P. A. Smith, the authors prove that a periodic homeomorphism has a (nonvoid) continuum as its fixed point set. They then deduce possible periods for homeomorphisms on tree-like continua which satisfy certain decomposability or irreducibility conditions. The main result of the paper is that a compact group of homeomorphisms has a continuum as its fixed point set. This is applied to isometries. The paper concludes with sufficient conditions that a pointwise periodic homeomorphism have a fixed point.

Continua admitting arc-structures and arc-smooth continua are introduced as higher dimensional analogues of dendroids and smooth dendroids, respectively. These continua include such spaces as: cones over compacta, convex continua in $ {l_2}$-spaces of Stadtlander. Known characterizations of smoothness in dendroids involving closed partial orders, the set function , radially convex metrics, continuous selections, and order preserving mappings are extended to the setting of continua with arc-structures. Various consequences of the special contractibility properties of arc-smooth continua are also obtained.

Several letters to the editor are presented in response to articles published in previous issues including the blog post "Cracking Down on Frenchmen Street Begins Anew," another letter on incredible help from people regarding relief for the earthquake on March 11, 2011 in Japan and a letter on music bands.