## Abstract

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

Original language | English |
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Pages (from-to) | 135-145 |

Number of pages | 11 |

Journal | Topology and its Applications |

Volume | 227 |

DOIs | |

State | Published - 15 Aug 2017 |

## Keywords

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

## ASJC Scopus subject areas

- Geometry and Topology

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