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Partitions into thin sets and forgotten theorems of Kunugi and Luzin–Novikov

Volume 155 / 2019

Edward Grzegorek, Iwo Labuda Colloquium Mathematicum 155 (2019), 267-285 MSC: 28A05, 54C10, 54E52. DOI: 10.4064/cm7287-4-2018 Published online: 10 December 2018


Let $f$ be a function from a metric space $Y$ to a separable metric space $X$. If $f$ has the Baire property, then it is continuous apart from a 1st category set. In 1935, Kuratowski asked whether the separability requirement could be removed. A full scale attack on the problem took place in the late seventies and early eighties. What was not known then, and what remains virtually unknown today, is that a first impressive attempt to solve the Kuratowski problem, due to Kinjiro Kunugi and based on a theorem of Luzin and Novikov, had already taken place in 1936. Luzin’s remarkable 1934 Comptes Rendus note, soon forgotten, has remained unnoticed to this day. We analyze both papers and bring the results to full light.


  • Edward GrzegorekInstitute of Mathematics
    University of Gdańsk
    Wita Stwosza 57
    80-308 Gdańsk, Poland
  • Iwo LabudaDepartment of Mathematics
    The University of Mississippi
    University, MS 38677, U.S.A.

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