Life cycle considerations and design options are hardly quantitatively taken into consideration during the conceptual design phase. In order to overcome this deficiency, a general theoretical framework is developed in this paper. In this paper design activity is analyzed via topology. At first in the second section, the basic semantic used in this research is defined from an intentional viewpoint. In the third section, we use the axiom 4 of the General Design theory to show that an order exists on the topological spaces. In that perspective, we show the practical interest of a two steps approach- at first a systematic description of the design problem using classifications, followed by the use of dimensional analysis in order to obtain a metric space. Afterwards, using the example of a pressure regulator, we show that the framework helps in generating concepts, simulating the behavior of such concepts and modeling the entire life cycle. In order to model the entire life cycle two proposals are made in this article. The first one consists of adding three new quantities and units to the SI system, for the reason that, engineering design is dealing with the technical performances of the products but also with three other quantities respectively the information, the environmental impact and the monetary quantity. The concept of information is used to measure the three different types of complexity defined in this research respectively the macro-geometrical, micro-geometrical, and material complexity. The unit used to measure these attributes is the Shannon (sh). The environmental impact quantity is measured via the derived quantity called entropy. The unit of entropy is related to four base units respectively M.L2 ·.t−2 .T−1 with respectively M: Mass, L: Length, t: Time and T: Temperature. The monetary quantity is measured using the Euro (€). Theoretical aspects relating to these choices are investigated in this paper. The second original proposal consists of using systematically the dimensional analysis theory in order to ensure the topological transformation from the physical problem into a mathematical one. Moreover dimensional analysis should become a powerful tool for comparing concepts and diminishing the problem complexity. This framework is applied in order to treat respectively the physical, the economical and the environmental aspects associated with the design problem.