Homeomorphisms of R and the Davey Space

On Periodic Shadowing Property

In this paper, some properties of the periodic shadowing are presented. It is shown that a homeomorphism has the periodic shadowing property if and only if so does every lift of it to the universal covering space. Also, it is proved that continuous mappings on a compact metric space with the periodic shadowing and the average shadowing property also have the shadowing property and then are chao...

On category of co-coverings

In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for the covering concept. For example, we provide the lifting criterion for co-coverings of a topological space X, which helps us to classify them by subgroups of the group of all homeomorphisms of X.

On bD-Sets and Associated Separation Axioms

Groups not acting on compact metric spaces by homeomorphisms

We show that the direct sum of uncountably many nonAbelian groups does not embed into the group of homeomorphisms of a compact metric space. The main result of this note does not seem to exist in the literature. Among other things, it provides simple examples of left-orderable groups of continuum cardinality which do not embed in Homeo+(R). Theorem 1.1. Let X be a compact metric space, I be an ...

Collin Bleak

My research primarily uses close analysis of the dynamics of a group or semigroup action on a space to discern properties of the group or semigroup. In particular, I am primarily interested in groups of automorphisms of a space and in semigroups of endomorphisms of a space. Supporting this, I have a secondary focus on topological and symbolic dynamics, which itself has lead me to an interest in...