On a problem posed by M. M. Popov

Volume 211 / 2012

F. Albiac, J. L. Ansorena Studia Mathematica 211 (2012), 247-258 MSC: 46A16, 46G05, 46G10. DOI: 10.4064/sm211-3-6


We show that if $X$ is a non-locally convex quasi-Banach space with a rich dual, there exists a continuous function $f:[0,1]\to X$ failing to have a primitive. This answers a twenty year-old question raised by M. Popov in this journal.


  • F. AlbiacMathematics Department
    Universidad Pública de Navarra
    Pamplona, 31006 Spain
  • J. L. AnsorenaDepartment of Mathematics
    and Computer Science
    Universidad de La Rioja
    Logroño, 26004 Spain

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