Linear continuous surjections of Cp-spaces over compacta

Kazuhiro Kawamura, Arkady Leiderman

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Let X and Y be compact Hausdorff spaces and suppose that there exists a linear continuous surjection T:Cp(X)→Cp(Y), where Cp(X) denotes the space of all real-valued continuous functions on X endowed with the pointwise convergence topology. We prove that dim⁡X=0 implies dim⁡Y=0. This generalizes a previous theorem [7, Theorem 3.4] for compact metrizable spaces. Also we point out that the function space Cp(P) over the pseudo-arc P admits no densely defined linear continuous operator Cp(P)→Cp([0,1]) with a dense image.

Original languageEnglish
Pages (from-to)135-145
Number of pages11
JournalTopology and its Applications
Volume227
DOIs
StatePublished - 15 Aug 2017

Keywords

  • C-theory
  • Dimension
  • Hereditarily indecomposable continua
  • Linear operators

ASJC Scopus subject areas

  • Geometry and Topology

Fingerprint

Dive into the research topics of 'Linear continuous surjections of Cp-spaces over compacta'. Together they form a unique fingerprint.

Cite this