SURFACES

0. Introduction. Let X be a Klein surface [1], that is, X is a surface with boundary 3X together with a dianalytic structure on X. The surface X need not be orientable. A homeomorphism f: X--> X of X onto itself that is dianalytic will be called an automorphism of X. In a recent paper [10] we showed that a compact bordered Klein surface of (algebraic) genus g •> 2 cannot have more than 12(g- 1