The concept space is large, unexplored and open. Concept structures to preserve and analyze database concepts are focused, and the properties of concepts completeness and classes/concepts completeness are introduced. Outside the space where structures preserving and analyzing database concepts are located, incompleteness holds. Exploiting these properties as reference points for the location of concepts and concept structures in the space, a frame is proposed. Not all the concept structures can be linked with the scientific domain of computer science. In the open concept space, both formal and informal concept structures are located. These can be complete, incomplete, not necessarily related to computer science. An example of the frame applicability is given.