Pure Mathematics and Applications
Pseudographs, Incidence Relation, Digital Topology, Abstract Complexes
Incidence pseudographs model a (re°exive and symmetric) inci- dence relation between sets of various dimensions, contained in a count- able family. Work by Klaus Voss in 1993 suggested that this general discrete model allows to introduce a topology, and some authors have done some studies into this direction in the past (also using alternative discrete models such as, for example, abstract complexes or orders on sets of cells). This paper provides a comprehensive overview about the topology of incidence pseudographs. This topology has various appli- cations, such as in modeling basic data in 2D or 3D digital picture analysis, or in describing polyhedral complexes. This paper addresses especially also partially open sets which occur, for example, in common (non-binary) picture analysis.
James, Thomas R. and Klette, Reinhard, "The Topology of Incidence Pseudographs" (2010). Mathematics Faculty Scholarship. 22.
James, Thomas R. Klette, Reinhard. “The Topology of Incidence Pseudographs.” Pure Mathematics and Applications 20.1-2 (2010): 77-101.