ABSTRACT
The proofs of existence, stability and uniqueness are important topics for the research of general equilibrium theory. In the 1950s, the proof of the existence of a general equilibrium utilized topology and fixed-point theorems or set theory and the convex set method, which were mathematical tools different from those used for the proof of stability (like Liapunov theory). Japanese mathematician Seiji Takizawa gave an intuitive exposition and said:
Topology is the geometry that studies unchangeable characteristics in oneto-one bicontinuous transformations (both mapping and reverse mapping are continuous). Roughly speaking, it is the geometry on an elastic plane. It considers if two points are connected and does not care about whether the lines are straight or curved, long or short.
(Takizawa 1991, in Japanese: 1067, my translation)
