Browsing by Author "Smith, Michel"

This paper is a brief survey of hyperspaces of topological spaces. In particular, the hyperspace of all nonempty compact subsets of a space and the hyperspace of all nonempty subcontinua of a space with the Vietoris topology. ...

In the present dissertation the study of flows on n-manifolds in particular in dimension three, e.g., R^3, is motivated by the following question. Let A be a compact invariant set in a flow on X. Does every neighbourhood ...

The majority of the research in quantum computation theory is based on quantum mechanical systems consisting of quantum subsystems that are all of the same dimension. Following and expanding on the research conducted by ...

Given a set \(F\) of functions that have their domain and codomain in common, if the codomain is ordered we may partially order \(F\) by choosing a subset \(S\) of their domain and saying that for \(f,g \in F\), \(f \leq ...

A topological game G(X) is a two-player game which characterizes properties of a topological space X based upon the existence of winning perfect-information strategies for players in the game. If the property P is ...

We present here constructions, both smooth and piecewise-linear, of non-singular, measure-preserving dynamical systems on R3, with each trajectory contained in a bounded set. In the smooth case, we use a sequence of nested ...

Inverse limit spaces have been a topic studied in various fields of mathematics such as Algebra, Measure Theory, and Topology. Here, we present a theorem that can be summarized as a game in which a given compact metric ...

The author describes in detail the construction of a Peano continuum which is homogeneous and non-bihomogeneous. This continuum was originally constructed by G. Kuperberg in the paper Another homogeneous, non-bihomogeneous ...

A continuum X is said to be decomposable if it can be written as a union of two proper subcontinua; otherwise, X is said to be indecomposable. For years, topologists have used inverse limits with continuous bonding functions ...

An introduction to the Stone-Čech compactification $\beta X$ of a normal topological space $X$ is given. The method of invariantly embedding linear orders into ultrapowers is used to find $2^{\mathfrak{c}}$ pairwise ...