On the Eüler Characteristic of Polyhedra

1. The principal object of this note is to give an extremely simple axiomatic characterization of the Euler characteristic for finite polyhedra. The idea of the construction used was suggested by the definition of the Grothendieck group of sheaves over a space [l]. Unless otherwise noted, "space" always means "triangulable space with base point," and a "pair" is a "triangulable pair of spaces with common base point." Mappings of spaces always preserve base points. If (X, 4) is a pair, then X/A denotes the space obtained from X by identifying 4 to a point.