The invention relates to a container having a head piece (7), which container can be or is filled with a medium and is produced of plastic materials using a blow molding, filling, and sealing method, comprising a transition region (13) between the container (1) and at least one first type of a head surface (11), which is arranged on the head piece (7) at an end face and can be penetrated by means of a piercing or cutting part and extends with a specifiable curvature. Said container is characterized in that at least one second type of a head surface (41), which likewise has a specifiable. curvature, which is the same as the curvature of the head surface (39) of the first type, but preferably is different therefrom, is present on the head piece (7), that the head surfaces transition into each other in such a way that a whole surface is formed, which spans the free end of the transition region (13) directed away from the container (1), and that the head piece (7) is an integral component of the container (1).
