The connector (1) has a connection region (3a) for connecting a medical substance container (2) i.e. glass bottle, and a channel (7) extending form an end section (6a) to another end section (6b) of a piercing element (4) i.e. tube, for conveying medical substance. The former end section of the piercing element pierces a membrane (8) of the container connected to the connection region. A dawning element (5) is deformably and/or breakably fixed at the latter end section. The dawning element closes the channel in a fluid-tight manner in a fastened state. The connection region is formed as a luer lock.
