A package comprising a container including a bowl formed to include an interior product-storage region and a brim coupled to an upper portion of the bowl and arranged to border an opening into the interior product-storage region, the brim including a radially outwardly facing side surface arranged to surround the upper portion of the bowl and an endless upwardly facing top surface arranged to lie between the upper portion of the bowl and the radially outwardly facing side surface, and a closure configured to mount on the brim in a closed position to close the opening and block access to the interior product-storage region formed in the bowl and to be removed by a consumer to gain access to the interior product-storage region, the closure including a sheet-support ring arranged to mate with the brim when the closure is positioned to lie in the closed position on the brim, the sheet-support ring including an endless upwardly facing top surface arranged to lie adjacent to a portion of the endless upwardly facing top surface of the brim when the closure is positioned to lie in the closed position on the brim, and the closure further including a membrane sheet coupled to the sheet-support ring to move therewith relative to the brim of the container when the closure is separated from the brim to gain access to the interior product-storage region, wherein the membrane sheet includes a ring-shaped outer portion bonded permanently to the sheet-support ring to form an endless seal therebetween, a central portion surrounded by the ring-shaped outer portion and arranged to cover the opening into the interior product-storage region when the closure is positioned to lie in the closed position on the brim, and a ring-shaped middle portion arranged to interconnect an outer perimeter edge of the central portion and an inner perimeter edge of the ring-shaped outer portion, the ring-shaped middle portion includes a downwardly facing surface arranged to overlie and confront a bonding portion of the endless upwardly facing top surface of the brim, and the package further comprises means for bonding the downwardly facing surface of the ring-shaped middle portion of the membrane sheet temporarily to the bonding portion of the upwardly facing top surface of the brim to establish an endless hermetic seal therebetween that remains until the closure is removed from the brim by a consumer for a first time to gain access to product stored in the interior product-storage region, and characterized in that an inner perimeter edge of the upwardly facing top surface of the sheet-support ring of the closure is arranged to surround and lie in spaced-apart relation to an outer perimeter edge of the upwardly facing top surface of the brim of the container to form a ring-shaped space therebetween, and in that the ring-shaped middle portion of the membrane sheet includes a ring-shaped anchor portion (22B1) coupled to the outer perimeter edge of the central portion and formed to include the downwardly facing surface confronting the bonding portion of the upwardly facing top surface of the brim and a ring-shaped bridge portion (22B2) arranged to lie between and interconnect the inner perimeter edge of the ring-shaped outer portion and the ring-shaped anchor portion (22B1) and to lie in an unsupported position over and across the ring-shaped space provided between the upwardly facing top surfaces (24U, 18U) of the sheet-support ring and the brim.