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The fundamental groupoid of the quotient of a Hausdorff space by a discontinuous action of a discrete group is the orbit groupoid of the induced action
Ronald Brown, Philip J. Higgins
The main result is that the fundamental groupoid of the orbit space of a discontinuous action of a discrete group on a Hausdorff space which admits a universal cover is the orbit g…
Geometric Aspects of Multiagent Systems
Timothy Porter
Recent advances in Multiagent Systems (MAS) and Epistemic Logic within Distributed Systems Theory, have used various combinatorial structures that model both the geometry of the sy…
What `shape' is space-time?
Timothy Porter
Some examples from the mathematics of shape are presented that question some of the almost hidden assumptions behind results on limiting behaviour of finitary approximations to spa…
Universal groups for point-sets and tilings
Johannes Kellendonk, Mark V Lawson
We study the universal groups of inverse semigroups associated with point sets and with tilings. We focus our attention on two classes of examples. The first class consists of poin…
Computation and Homotopical Applications of Induced Crossed Modules
Ronald Brown, Christopher D. Wensley
We explain how the computation of induced crossed modules allows the computation of certain homotopy 2-types and, in particular, second homotopy groups. We discuss various issues i…