Dedekind’s Map-theoretic Period

Abstract

In 1887–1894, Richard Dedekind explored a number of ideas within the project of placing mappings at the very center of pure mathematics. We review two such initiatives: the introduction in 1894 of groups into Galois theory intrinsically via field automorphisms, and a new attempt to define the continuum via maps from ℕ to ℕ (later called Baire space) in 1891. These represented the culmination of Dedekind's efforts to reconceive pure mathematics within a theory of sets and maps and throw new light onto the nature of his structuralism and its specificity in relation to the work of other mathematicians.

from # All Medicine by Alexandros G. Sfakianakis via Alexandros G.Sfakianakis on Inoreader http://ift.tt/2hYLJCT
via IFTTT