Interaction between General Topology and Functional Analysis

Abstract

This paper concerns the history of the interaction between topology and analysis. As a theory, topology began in 1847 (Sec. 1, Listing). The first phase (1847–1887) was a development of topology under the influence of classical analysis, in particular, complex analysis (Sec. 2, Riemann) and the calculus of variations (Sec. 3, Weierstrass). General set theory was born in 1874 (Sec. 2, Cantor). This was the necessary starting point of set-theoretic topology (also called general topology), which plays a greater role in analysis than combinatorial topology (initiated by Poincare) and algebraic topology do (Sec. 5).