An inductive component, for the formation of a magnetic circuit has at least one wire winding and at least one core with a ferromagnetic core material. The core comprises a gap and at least one further gap to interrupt the magnetic circuit. The inductive component is characterized in that the gaps each have a gap width of at least 1.0 mm. The core comprises two pieces, for example, which are arranged opposed to each other across the gaps and separated from each other by the gap width. The component is advantageously symmetrical with an essentially equal gap width for the gaps. A miniaturized inductive component is possible by the use of a hire winding made from high frequency braided wire and core material capable of accepting high frequencies, which has a high Q-factor even on a high power throughput and thus low electrical losses. In order to increase the Q-factor, the inductive component also has a cooling device for cooling the wire winding. The device is thus provided with a composite material with a thermally-conducting filler. The inductive component is used in a so-called electronic ballast (EVG) in the field of illumination.