A constructive treatment of Urysohn's Lemma in an apartness space
Douglas Bridges, Hannes Diener · Mathematical logic quarterly · 2006
Abstract This paper is dedicated to Prof. Dr. Günter Asser, whose work in founding this journal and maintaining it over many difficult years has been a major contribution to the activities of the mathematical logic community. At first (maybe even at second) sight it appears highly unlikely that Urysohn's Lemma has any significant constructive content. However, working in the context of an apartness space and using functions whose values are a generalisation of the reals, rather than real numbers, enables us to produce a significant constructive version of that lemma. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)