The anti-Specker property, a Heine-Borel property, and uniform continuity
The paper contributes to the ongoing program of constructive reverse mathematics. It investigates a very weak version of the Heine-Borel property for subsets of the real line. It is shown that this property is satisfied whenever the space satisfies a strong antithesis of the existence of a Specker sequence (that is, a bounded sequence of real numbers that does not converge). The latter property can be seen as an intuitionistic version of sequential compactness. Furthermore reasons are given why the converse does not hold. The paper then continues and investigates the relations between the two above-mentioned principles and the uniform continuity principle for integer-valued functions. The paper is of relevance to anybody interested in (constructive) reverse mathematics, recursive/constructive analysis and foundational issues related to the continuum.
scientific article; zbMATH DE number 5278972
scientific article