A generic topology library

AbstractRequirements in scientific computing emerge from various areas such as algebraic topology, geometrical algebra, and differential topology with different notations. Cell and complex properties are introduced in order to derive a common specification for properties of data structures. Only topological properties are used, thereby separating the actual data storage structure from the stored data. Several theoretical topological properties are introduced, and traversal capabilities which excel current implementations are presented and accompanied by selected examples.This work focuses on extracting these necessary mathematical concepts and introduces generic programming concepts necessary to fully transfer the mathematical concepts. Not only theoretical contributions are presented, but they are also demonstrated by means of applications in scientific computing