Topology changes of spherical lipid Vesicles to coffee cups (Saitoh, A. et al, Proc. Natl. Acad. Sci. USA 95, 1026 (1998)) were analyzed by a statistical mechanical theory. The topology change was due to the adsorption of talin molecules to the orifices of the coffee cups. The equilibrium is determined by the balance of the energy gain for the adsorption of talin to the periphery of the vesicles and the change of the bending energy of the membrane due to the shape change. The observed coexistence of coffee cups and sheet-like vesicles were reproduced.