A mirror with a mirror carrier, as well as related apparatuses, systems and methods are disclosed. The mirror carrier can be embodied as cooling device with at least one cooling channel. Tube connections can be provided to connecting the at least one cooling channel to an inlet and an outlet of coolant. Sealing elements for a gas-tight and liquid-tight seals can be arranged between the tube connections and the mirror carrier. The field of application of the mirror can be, for example, an illumination device of a projection exposure apparatus.