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Archiv der Mathematik

, Volume 80, Issue 6, pp 655–663 | Cite as

Note on function spaces with the topology of pointwise convergence

  • Jan van Mill
  • Jan Pelant
  • Roman Pol
Original paper

Abstract.

The note contains two examples of function spaces C p (X) endowed with the pointwise topology. The first example is C p (M), M being a planar continuum, such that C p (M) m is uniformly homeomorphic to C p (M) n if and only if m = n. This strengthens earlier results concerning linear homeomorphisms. The second example is a non-Lindelöf function space C p (X), where X is a monolithic perfectly normal compact space all linearly orderable closed subspaces of which are metrizable. This example is obtained under the additional set-theoretical axiom ◊. This solves a problem of Arhangel’skiĭ.

Mathematics Subject Classification (1991):

54C35 

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Copyright information

© Birkhäuser-Verlag 2003

Authors and Affiliations

  1. 1.Division of Mathematics and Computer ScienceVrije UniversiteitAmsterdamThe Netherlands
  2. 2.Mathematical Institute AV ČRPraque 1Czech Republic
  3. 3.Warsaw UniversityWarsawPoland

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