Abstract

In the pointwise topology, familiar function spaces Cp(βN)C_{p}(\beta\mathbb{N}), Cp(R)C_{p}(\mathbb{R}), Cp[0,1]C_{p}\left[ 0,1\right], and Cp(Cantor set)C_{p}(\text{Cantor set}) are not distinguished.

Author information

Contact details are reproduced from the original publication and may be historical.

Juan Carlos Ferrando

Centro de Investigación Operativa, Universidad Miguel Hernández, 03202 Elche, Spain

jc.ferrando@umh.es

Jerzy Kąkol

Faculty of Mathematics and Informatics, A. Mickiewicz University, 61-614 Poznań, Poland
and: Institute of Mathematics, Czech Academy of Sciences, Prague, Czech Republic

kakol@amu.edu.pl

Keywords

  • Distinguished locally convex space
  • pointwise topology
  • strongest locally convex topology
  • function spaces

Mathematics Subject Classification

46A08, 46E10; 54C35

References

  1. J. C. Ferrando, J. Kąkol: Metrizable bounded sets in C(X) spaces and distinguished Cp (X) spaces, J. Convex Analysis 26(4) (2019) 1337–1346.https://doi.org/10.68381/jca26070Google Scholar
  2. J. Kąkol: Cp -spaces dominated by metrizable topologies, Topology Appl. 265 (2019), to appear.https://doi.org/10.1016/j.topol.2019.106837Google Scholar
  3. E. Michael: ℵ0 -spaces, J. Math. Mech. 15 (1966) 983–1002.https://doi.org/10.1512/iumj.1966.15.15066Google Scholar

Suggested citation

J. C. Ferrando, J. Kąkol, S. A. Saxon. “Examples of Nondistinguished Function Spaces C_p(X).” Journal of Convex Analysis 26 (2019), No. 4, 1347–1348. https://doi.org/10.68381/jca26071

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Published by Heldermann Verlag, 2019. Rights now held by Banach Press LLC.