The invention is directed to a building comprising more than one separate spaces and an air treatment system. The air treatment system comprises a central air drying unit fluidly connected to two or more local evaporative cooling units, wherein at least two local evaporative cooling units are each fluidly connected to a separate space of the building. The invention is also directed to a method to cool the air in two or more separate spaces by (a) drying ambient air in a central air drying unit to obtain a volume of dried air, (b) drawing in a part of the volume of dried air as obtained in step (a) to each separate space by means of an air displacement means and (c) using the dried air in a process of indirect evaporative cooling to obtain cooled air which is discharged into the interior of the separate space.