### Abstract

For each non-quadratic p-adic integer, p > 2, we give an example of a torus-like continuum Y (i.e., inverse limit of an inverse sequence, where each term is the 2-torus T^{2} and each bonding map is a surjective homomorphism), which admits three 4-sheeted covering maps f_{0}: X_{0} → Y, f_{1}: X_{1} → Y, f_{2}: X_{2} → Y such that the total spaces and X_{0} = Y, X_{2} are pair-wise non-homeomorphic. Furthermore, Y admits a 2p-sheeted covering map f_{3}: X_{3} → Y such that X_{3} and Y are non-homeomorphic. In particular, Y is not a self-covering space. This example shows that the class of self-covering spaces is not closed under the operation of forming inverse limits with open surjective bonding maps.

Original language | English |
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Pages (from-to) | 359-369 |

Number of pages | 11 |

Journal | Topology and its Applications |

Volume | 153 |

Issue number | 2-3 SPEC. ISS. |

DOIs | |

Publication status | Published - 2005 Sep 1 |

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### Keywords

- Covering mapping
- Direct system
- H-connected space
- Inverse system
- p-adic number
- Quadratic number
- Torsion-free group of rank 2
- Torus-like continuum

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Topology and its Applications*,

*153*(2-3 SPEC. ISS.), 359-369. https://doi.org/10.1016/j.topol.2003.06.006