ABSTRACT
Kurt Lewin's book Principles of Topological Psychology is deeply flawed. Lewin in reality does not utilize one single theorem of topology. In the late 1960s, several mathematicians read Lewin and took up the project of bringing actual mathematical methods to bear on his subject matter. There are important differences among, on the one hand, the mathematical models of "life spaces" that this chapter proposes to construct, and, on the other, both the class of mathematical models based on the real-number system, and premathematical models like those actually given by Lewin. That a life space is "constructed," and that there can be a multiplicity of such constructions, is a major distinction between life spaces and Umwelts. Any number of mathematical ideas introduced by Lewin into his discussions of life spaces—for instance, the notion of "boundary of a region".
