Topological fractals revisited

The uploaded paper proves that every Peano continuum with uncountably many local cut points is a topological fractal and that five maps suffice (Theorem 17), via the construction of a free Cantor set (Definition 7) and explicit use of an upper semicontinuous selection/General Mapping Theorem to build maps whose iterates shrink diameters; it also treats the special case of uncountably many global cut points with three maps (Theorem 14). These ingredients appear explicitly across Definition 1, Lemmas 12, 13, 15–16, Observation 6, and Theorems 14 and 17 in the text . The candidate solution reproduces this scheme: (i) builds a binary-indexed ‘free Cantor set’ structure from uncountably many (local) cut points, (ii) uses Nadler’s General Mapping Theorem to obtain finitely many continuous maps, and (iii) argues uniform diameter shrink of iterates; it also notes that five maps suffice in general and three in the global-cut-point case. Minor issues: the candidate asserts each witnessing map is surjective onto X (stronger than needed and not what the paper proves) and mentions a possible reduction to two maps without support here. Aside from those, the approach, logic, and core constructions match the paper’s proof.