Compared to single extraction units, where the mist of a machine tool is extracted and purified by one single mist collector, central extraction systems are clear advantage for extraction and air purifying of multiple machine tools: The individual machine tools are connected via a pipe system with a centralized AFS air purification device. Using a duct system, the purified outgoing air is routed to an HVAC system and blown to the outside year-round as outgoing air. When necessary, a heat exchanger in the HVAC system mostly draws the residual heat from the exhaust air and uses it to preheat the cool outside air. The outside air, which is aspirated by the HVAC system, is filtered and (when necessary) preheated by the heat exchanger. If the preheating in the heat exchanger is insufficient (e.g., lack of heat in the outgoing air or when outside temperatures are extremely cold), then a reheating register also heats the outside air to the target temperature. The supply air can be air-conditioned by an additional cooling register in the HVAC system. The supply air is then routed to the hall by way of a defined duct system and distributed evenly and draught-free through outlet louvres or air diffusers. Exhaust and supply air systems are operated automatically using intelligent control and adjustment technology. Time programs enable different operating modes. Protecting the hall from cooling down during production downtimes can also be achieved as well as nighttime atmospheric cooling in summer. Using an AFS exhaust system with supply air system, clean, pollen-free and dust-free air that is optimally conditioned for the hall is supplied year-round.