An apparatus for establishing a connection having material continuity or having material continuity and shape matching or for separating such a connection of at least one metal or ceramic component and of a component formed from or by a thermoplastic polymer, with which the components (1 and 2) to be joined together can be pressed together by a pressing device having a counterholder and a plunger; and with which a heating device is present at the plunger and/or at the counterholder or acts there, with which heating device a heating of the at least one metal or ceramic component up to above the softening temperature of the component formed from or by the polymer can be achieved, wherein the heating device is formed by at least one electrical resistance heating element that is covered by an electrically insulating protective film, and/or having at least one laser beam that is directed to the metal component(s) within the joining region; and/or having at least one inductor present at the plunger and/or at the counterholder for the inductive heating of the metal component(s) (1,2). characterized in that a locally defined heating of the metal or ceramic component(s) in the joining region can be achieved by the heating device in that a plurality of electrical resistance heating elements are each individually controllable and in so doing are configured in the form of dot-shaped, linear, rectangular and/or circular ring segment-shaped electrical resistance heating elements with which an at least almost homogeneous temperature field within the joining region can be achieved; and/or the at least one laser beam can be deflected and/or operated in dependence on a temperature measurement device detecting with spatial resolution such that an at least almost homogeneous temperature field can be reached in the joining region; and/or the at least one inductor is designed as operable in a movable or regulable manner with respect to the metal component so that an at least almost homogeneous temperature field can be achieved in the joining region. with which a heating device is present at the plunger and/or at the counterholder or acts there, with which heating device a heating of the at least one metal or ceramic component up to above the softening temperature of the component formed from or by the polymer can be achieved, wherein the heating device is formed by at least one electrical resistance heating element that is covered by an electrically insulating protective film, and/or having at least one laser beam that is directed to the metal component(s) within the joining region; and/or having at least one inductor present at the plunger and/or at the counterholder for the inductive heating of the metal component(s) (1,2). characterized in that a locally defined heating of the metal or ceramic component(s) in the joining region can be achieved by the heating device in that a plurality of electrical resistance heating elements are each individually controllable and in so doing are configured in the form of dot-shaped, linear, rectangular and/or circular ring segment-shaped electrical resistance heating elements with which an at least almost homogeneous temperature field within the joining region can be achieved; and/or the at least one laser beam can be deflected and/or operated in dependence on a temperature measurement device detecting with spatial resolution such that an at least almost homogeneous temperature field can be reached in the joining region; and/or the at least one inductor is designed as operable in a movable or regulable manner with respect to the metal component so that an at least almost homogeneous temperature field can be achieved in the joining region.