On linear continuous open surjections of the spaces Cp(X)

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9 Scopus citations

Abstract

Solving a problem by Arkhangel'skiǐ, we construct a linear continuous open surjection L: Cp(X) → Cp(Y) for compacta X and Y with 0 < dim X < dim Y < ∞. An example of nonopen linear continuous surjection of the space Cp[0, 1] onto itself is given. Related topics and results are discussed.

Original languageEnglish
Pages (from-to)269-279
Number of pages11
JournalTopology and its Applications
Volume81
Issue number3
DOIs
StatePublished - 1 Jan 1997

Keywords

  • Basic embeddings
  • Continua
  • Dimension
  • Free locally convex spaces
  • Pointwise topology
  • Spaces of continuous functions

ASJC Scopus subject areas

  • Geometry and Topology

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