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