Retracing Cantor's first steps in Brouwer's company

We prove intuitionistic versions of the classical theorems saying that all countable closed subsets of [−π,π] and even all countable subsets of [−π,π] are sets of uniqueness. We introduce the co-derivative extension of an open subset of the set R of the real numbers as a constructively possibly more useful notion than the derivative of its complement, a closed subset of R. We also have a look at an intuitionistic version of Cantor's theorem that a closed set is the union of a perfect set and an at most countable set.