Partitions into thin sets and forgotten theorems of Kunugi and Luzin-Novikov
Edward Grzegorek , Iwo Labuda
AbstractLet 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.
|Journal series||Colloquium Mathematicum, ISSN 0010-1354, , (A 15 pkt)|
|Publication size in sheets||0.9|
|Keywords in English||Baire category, Baire property, 2nd countable topological space, function continuous apart from a 1st category set, Borel measure, measurable set, outer measure, measurable envelope|
|Score|| = 15.0, ArticleFromJournal|
= 15.0, ArticleFromJournal
|Publication indicators||: 2017 = 0.42 (2) - 2017=0.535 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.