## Abstract

Let C_{P}(X) be the space of continuous real-valued functions on X, with the topology of pointwise convergence. We consider the following three properties of a space X: (a) C_{P}(X) is Scott-domain representable; (b) C_{P}(X) is domain representable; (c) X is discrete. We show that those three properties are mutually equivalent in any normal T_{I}-space, and that properties (a) and (c) are equivalent in any completely regular pseudo-normal space. For normal spaces, this generalizes the recent result of Tkachuk that C_{p}(X) is subcompact if and only if X is discrete.

Original language | English |
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Pages (from-to) | 185-199 |

Number of pages | 15 |

Journal | Fundamenta Mathematicae |

Volume | 200 |

Issue number | 2 |

DOIs | |

State | Published - 2008 |

## Keywords

- Choquet complete
- Domain
- Domain representable space
- Normal space
- Pointwise convergence topology
- Pseudo-normal space
- Scott domain
- Scott topology
- Subcompact space

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