The Real Numbers in Pointfree Topology

This text, based on the lectures of a course presented at the University of Coimbra, and written in a very didactic and engaging style, is a careful and innovative exposition of the pointfree theory of rings of continuous real functions and its constructive aspects. A global treatment of pointfree continuous real functions puts them in a new perspective. Highlights of the book include an in-depth treatment of the Stone-Weierstrass theorem and its applications to functional analysis. The material appeared in book form for the first time in the previous collection Textos de Matemática Universidade de Coimbra (vol. 12), and became the main reference on the topic. Three appendices provide the necessary background on concepts from logic, ordered rings and uniform structures. The present edition has been carefully revised and expanded. It includes an essay on the author’s mathematical career, style, and impact on mathematics by Karl Heinrich Hofmann (Darmstadt), as well as an interview with the author, conducted by Christopher Gilmour (Cape Town). The list of Bernhard Banaschewski’s publications is also included, showing his contributions to an impressive number of areas.