A TOPOLOGICAL GEOMETRICAL APPROACH TO THE STUDY OF ASTROPHYSICAL MAPS

This paper discusses topological and geometrical methods for analyzing astrophysical maps, ranging from emission maps of molecular clouds to surveys of the large-scale structure of the universe. We construct a formalism which considers the collection of all maps of a given type as a metric space; we then construct a set of distance functions (pseudometrics) which measure the difference between any two astrophysical maps and thereby topologize the space of maps. We use these pseudometrics to construct a procedure for ordering the space of maps. The results of this work provide a formalism for analyzing and classifying astrophysical maps.