Mathematical concepts applied to painting, as well as to architectural design, arise frequently from intuition. The important role they play in design processes is being currently vindicated, as it is evidenced by artists and mathematicians as Lucio Saffaro. Topology is concerned with the properties of spaces that are preserved under continuous deformations, and has proved to be particularly useful in the previous stages of the architectural projects, when the location of uses and itineraries is defined. On the other hand, topology brings lots of possibilities in those phases of design where no dimensional definition is needed, but just to satisfy some spatial properties. It becomes then a powerful easy tool to show and analyse different solutions by means of their spatial relationships. Concepts as adjacency, connectedness, intersection, or inclusion, can be directly applied to layout schemes, setting the basis to further dimensioning. These concepts are traditionally managed and implemented by Geographic Information Systems (GIS), and are now being applied to architecture by means of Building Information Models (BIM). As a particular use, the architectural design of hospitals and other health care facilities benefits directly from topology’s properties. It is due, firstly, to their high complexity derived from their particular technical, functional, and equipment constraints. Secondly, topology becomes helpful to design the inner and outer itineraries of both people and logistics, paying attention to the specific problems derived from transfer points, pollution risks, and intersections. And thirdly, it permits to take into account the various possible users: patients, visitors, accompanying persons, staff, logistics suppliers, etc. The case study is a result of the research project (BIA2016‒78893‒C3‒1‒R) funded by the Spanish Ministry of Economy, Industry and Competitiveness, and the EU.
