We say that a Cantorval 𝑋 is achievable if there exists a convergent positive series Σ︀ 𝑢𝑛 such that 𝑋 = 𝐸(𝑢𝑛). Taking into account the above theorem, there naturally arises the question: Is the boundary 𝑋𝐶 for an arbitrary Cantorval 𝑋 a fractal set?