Possibly every real function is continuous on a non–meagre set. Shelah, S. Publications de L'Institute Mathématique - Beograd, Nouvelle Série, 57(71):47–60, 1995. arxiv:math/9511220
bibtex   
@article{Sh:473,
author = {Shelah, Saharon},
fromwhere = {IL},
journal = {Publications de L'Institute Math\'ematique - Beograd,
 Nouvelle S\'erie},
note = { arxiv:math/9511220 },
pages = {47--60},
title = {{Possibly every real function is continuous on a non--meagre
 set}},
volume = {57(71)},
year = {1995},
}

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