A closure assembly for mounting on a container includes a base configured for mounting on the container and defining an aperture through which the interior of the container is accessible. The base comprises a perimeter, a separator mounted on and extending across the perimeter with the aperture being formed in the separator, and a valve positioned on the separator. The valve extends across the aperture in the separator, and is openable by the application of pressure on the valve and self-closable upon removal of the pressure from the valve. The assembly also includes a cover for selectively covering the aperture. The cover is mounted on the base and is movable with respect to the base between a closed position and an open position. The closed position is characterized by the aperture not being accessible and the open position is characterized by the aperture being accessible.