Dini’s Theorem in the Light of Reverse Mathematics

摘要: Dini’s theorem says that compactness of the domain, a metric space, ensures uniform convergence every simply convergent monotone sequence uniformly continuous real-valued functions whose limit is continuous. By showing it equivalent to Brouwer’s fan for detachable bars, we provide with classification in constructive reverse mathematics recently propagated by Ishihara. If occurring are pointwise but integer-valued, then still obtain such need replace principle integer-valued function on Cantor space As complement, both and proved be analogue theorem, weak Konig’s lemma, classical setting started Friedman Simpson.