Skeletons and Central Sets

Let be an open proper subset of Rⁿ. Its skeleton is the setof points with more than one nearest neighbour in the complementof its central set is the set of centres in maximal open ballsincluded in . Intuitively, if we think of as a land mass inwhich height is proportional to distance from the sea, its skeletonand central set can be thought of as corresponding to ridgesin the mountains of . In this note I discuss the metric andtopological properties of such sets. I show that any skeletonin Rⁿ is F, and has dimension at most n – 1, by any ofthe usual measures of dimension; that if is bounded and connected,its skeleton and central set are connected; and that separatesRⁿ iff its skeleton does iff its central set does. Any centralset in Rⁿ is a G set of topological dimension at most n –1. In the plane, I show that both skeletons and central setsare locally path-connected, and indeed include many paths offinite length. For any , its central set includes its skeleton;I give examples to show that the central set can be significantlylarger than the skeleton. 1991 Mathematics Subject Classification:54F99.     

Inclusive and semi-inclusive ϱ0 production in π−p interactions at 15 GeV/c

We have done an inclusive study of ?⁰ production in π^?p interactions at 15 GeV/c. Evidence for two different production mechanisms, in addition to the known quasi two-body processes, is presented: production of ?⁰'s in the central region of rapidity similar to the “pionization” region seen in the inclusive studies of pions; and forward production in the beam dissociation region of rapidity. Cross sections and rapidity distributions for the ?⁰ are given inclusively and by topology, and the results are compared with similar studies at other energies and with other incident particles. Results are also presented for the semi-inclusive reaction π^?p → p?⁰ + X^? and the exclusive final state pπ^??⁰.