 The Cantor and Dedekind definitions of the real numbers relied implicitly on set theory, and can be seen in retrospect to involve the assumption of a Power Set principle. Both took as given the set of rational numbers, and for the definition of \(\mathbf{R}\) they relied on a certain totality of infinite sets of rational numbers (either the totality of Cauchy sequences, or of all Dedekind cuts). With this, too, constructivistic criticism of set theory began to emerge, as Leopold Kronecker started to make objections to such infinitary procedures. Simultaneously, there began a study of the topology of \(\mathbf{R}\), in particular in the work of Weierstrass, Dedekind, and Cantor. The set-theoretic approach was also exploited by several authors in the fields of real analysis and complex analysis (e.g., Hankel, du Bois-Reymond, H.J.S. Smith, U. Dini) and by Dedekind in joint work with Weber (1882), pioneering algebraic geometry.