A dispensing system is provided and can be embodied in a dispensing closure for a container having an opening. The system includes a unitary, resiliently flexible, molded valve array structure for being sealingly disposed on the container over the container opening. The valve array structure includes an impervious membrane. The valve array structure also includes a plurality of resiliently flexible, slit valves molded unitary with the membrane. Each valve has a normally closed dispensing orifice which opens when the pressure in the interior of the container exceeds the pressure on the exterior of the valve by a predetermined amount. The valves can be arranged to discharge parallel streams, diverging streams, or converging streams.