A. McCluskey

activity

20112020

collaborators

4 papers

math.GN2020

Topological transitivity in quasi-continuous dynamical systems

Jiling Cao, Aisling McCluskey

A quasi-continuous dynamical system is a pair $(X, f)$ consisting of a topological space $X$ and a mapping $f : X \to X$ such that $f^{n}$ is quasi-continuous for all $n \in N$ ,…

math.CT2015

Betweenness relations in a categorical setting

J. Bruno, A. McCluskey, P. Szeptycki

We apply a categorical lens to the study of betweenness relations by capturing them within a topological category, fibred in lattices, and study several subcategories of it. In par…

math.GN2012

$T o p (X)$ within $\px$ ]{When lattices meet topology: $T o p (X)$ within $\px$.}

Jorge L. Bruno, Aisling E. McCluskey

For a non-empty set $X$ , the collection $T o p (X)$ of all topologies on $X$ sits inside the Boolean lattice $\PP(\PP(X))$ (when ordered by set-theoretic inclusion) which in turn can…

math.GN2011

Topologies on $X$ as points in $2^{P (X)}$

Jorge L. Bruno, Aisling E. McCluskey

A topology on a nonempty set $X$ specifies a natural subset of $P (X)$ . By identifying $P (P (X))$ with the totally disconnected compact Hausdorff space…

Topological transitivity in quasi-continuous dynamical systems

Betweenness relations in a categorical setting

Top(X) within $\px$ ]{When lattices meet topology: Top(X) within $\px$.}

Topologies on X as points in 2P(X)

$T o p (X)$ within $\px$ ]{When lattices meet topology: $T o p (X)$ within $\px$.}

Topologies on $X$ as points in $2^{P (X)}$