A systematic generalization procedure for fixed-point theorems

The progress of mathematics often follows a standard path: the discovery of a new theorem, followed by a systematic exploration of that theorem. Two s tandard ways of exploring theorems are by weakening the hypotheses and stre ngthening the conclusion. This paper discusses another way to explore theor ems through the sharing of hypotheses, and develops this idea in the contex t of three classical fixed-point theorems: the Banach Contraction Principle , the Tarski Fixed-Point Theorem for complete lattices and the Brouwer Fixe d-Point Theorem for solid n-spheres.