Fréchet–Urysohn Spaces and Groups

  • Jerzy KąkolEmail author
  • Wiesław Kubiś
  • Manuel López-Pellicer
Part of the Developments in Mathematics book series (DEVM, volume 24)


This chapter deals with topological (vector) spaces satisfying some sequential conditions. We study Fréchet–Urysohn space (i.e., spaces E such that for each AE and each \(x\in\overline{A}\) there exists a sequence in A converging to x). The main result states that every sequentially complete Fréchet–Urysohn lcs is a Baire space. Since every infinite-dimensional Montel (DF)-space E is nonmetrizable and sequential, the following question arises: Is every Fréchet–Urysohn space in the class \(\mathfrak{G}\) metrizable?


Baire Space Countable Network Main Result State Urysohn Space Balance Neighborhood 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Jerzy Kąkol
    • 1
    Email author
  • Wiesław Kubiś
    • 2
    • 3
  • Manuel López-Pellicer
    • 4
    • 5
  1. 1.Faculty of Mathematics and InformaticsA. Mickiewicz UniversityPoznanPoland
  2. 2.Institute of MathematicsJan Kochanowski UniversityKielcePoland
  3. 3.Institute of MathematicsAcademy of Sciences of the Czech RepublicPraha 1Czech Republic
  4. 4.IUMPAUniversitat Poltècnica de ValènciaValenciaSpain
  5. 5.Royal Academy of SciencesMadridSpain

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