[en] The authors show a construction of the set of all pure states of any physical system. This set appears to be compact in a physically meaningful topology. The approach is based on quantum logic notions, but is ''constructive'' in the sense that the authors assume that their knowledge about a system increases when more and more experiments are performed and that the set of states is not given to them from the very beginning but is determined by their knowledge at any stage of the investigations. The set of all states is obtained when all possible experiments are performed, which may require an infinite number of experiments. In such a situation the set of all states exists only on an abstract and purely theoretical level but nevertheless is still compact, the authors claim, by their construction