Accounting Principles from a Topological Point of View

Abstract

Some GAAP established more than six centuries ago still apply in accounting systems with high probability of success. However, in order to ensure these principles attain a maximum level of sufficiency, unbiasedness, efficiency, and consistency (SUEC), we need to improve their definitions giving them a robust universal conceptualization. This paper proposes a mathematical statement of seven fundamental accounting principles, related to a company’s cash flow statements, describing p-entry accounting systems, for p=1,2,3,…,N. These systems are developed by means of equilibrium financial equations on topological spaces called simplicial complexes. Incidence algebraic structures as fundamental (co)homology groups are presented briefly to illustrate this new conceptualization.