Euler characteristics of digital wedge sums and their applications

Abstract

Many properties or formulas related to the ordinary Euler characteristics of topological spaces are well developed under many mathematical operands, e.g. the product property, fibration property, homotopy axiom, wedge sum property, inclusion-exclusion principle [E.H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966], etc. Unlike these properties, the digital version of the Euler characteristic has its own feature. Among the above properties, we prove that the digital version of the Euler characteristic has the wedge sum property which is of the same type as that for the ordinary Euler characteristic. This property plays an important role in fixed point theory for digital images, digital homotopy theory, digital geometry and so forth.