Important Note: This document represents the notes I have taken during the Point Set Topology lectures of Dr. Vladimir Uspenskiy during the Fall 2013 term at Ohio University. As such, while I have done my best, I make no guarantees (or even implications) that everything contained therein is accurate or complete. While the material is obviously not my original work, this document is and as such ...

Practical needs in the realm of Geographic Information Systems (GISs) have driven the efforts to investigate formal and sound methods to describe spatial relations. After an introduction of the basic ideas and notions of topology, a novel theory of topological spatial relations between sets is developed in which the relations are defined in terms of the intersections of the boundaries and inter...

Context One of the welfare and ethical challenges with tracking animals is ensuring that device removed from animal at conclusion study. However, for are not readily re-trapped, impact devices alternatives their retrieval rarely examined.Aims We compared retention time two types break-away mechanisms collars deployed on mainland quokkas (Setonix brachyurus).Methods tested a cotton thread (CT) w...

In this paper, we introduce a new concept in set-valued mappings which we have called condition $(UHS)$. Then, adding this condition to a new type of contractive set-valued mappings, recently has been introduced by Amini-Harandi [Fixed and coupled fixed points of a new type contractive set-valued mapping in complete metric spaces, Fixed point theory and applications, 215 (2012)], we prove that ...

Point set surfaces (PSS) are a smooth manifold surface approximation from a set of sample points. The surface definition is based on a projection operation that constructs local polynomial approximations and respects a minimum feature size. We present techniques for ray tracing PSSs. For the computation of ray-surface intersection the properties of the projection operation are exploited: The su...