Strong and Uniform Continuity – the Uniform Space Case
Douglas Bridges, Luminiţa Vı̂ţă · LMS Journal of Computation and Mathematics · 2003
Abstract It is proved, within the constructive theory of apartness spaces, that a strongly continuous mapping from a totally bounded uniform space with a countable base of entourages to a uniform space is uniformly continuous. This lifts a result of Ishihara and Schuster from metric to uniform apartness spaces. The paper is part of a systematic development of computable topology using apartness as the fundamental notion.