## Abstract

For a local po-space X and a base point x_{0} ∈ X, we define the universal dicovering space Π: X̃_{x0} → X. The image of Π is the future ↑ x_{0} of x_{0} in X and X̃_{x0} is a local po-space such that |π^{→} _{1} (X̃, [x_{0}], x_{1})| = 1 for the constant dipath [x_{0}] ∈ Π^{-1}(x_{0}) and x_{1} ∈ X̃_{x0}. Moreover, dipaths and dihomotopies of dipaths (with a fixed starting point) in ↑ x_{0} lift uniquely to X̃_{x0}. The fibers Π^{-1}(x) are discrete, but the cardinality is not constant. We define dicoverings P: X̂ → X _{x0} and construct a map φ: X̃_{x0} → X̂ covering the identity map. Dipaths and dihomotopies in X̂ lift to X̃_{x0}, but we give an example where φ is not continuous.

Original language | English |
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Journal | Homology, Homotopy and Applications |

Volume | 5 |

Issue number | 2 |

Pages (from-to) | 1-17 |

Number of pages | 17 |

ISSN | 1532-0073 |

DOIs | |

Publication status | Published - 1 Jan 2003 |

## Keywords

- Abstract homotopy theory
- Covering spaces
- Dihomotopy theory