Retracing Cantor’s first steps in Brouwer’s company

摘要

AbstractWe prove intuitionistic versions of the classical theorems saying that all countableclosedsubsets of[?π,π]and even all countable subsets of[?π,π]are sets of uniqueness. We introduce theco-derivative extensionof an open subset of the setRof the real numbers as a constructively possibly more useful notion than the derivative of its complement, a closed subset ofR. 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.]]>