### 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 |
---|---|

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 |

### Fingerprint

### 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

**Torus-like continua which are not self-covering spaces.** / Eda, Katsuya; Mandić, Joško; Matijević, Vlasta.

Research output: Contribution to journal › Article

*Topology and its Applications*, vol. 153, no. 2-3 SPEC. ISS., pp. 359-369. https://doi.org/10.1016/j.topol.2003.06.006

}

TY - JOUR

T1 - Torus-like continua which are not self-covering spaces

AU - Eda, Katsuya

AU - Mandić, Joško

AU - Matijević, Vlasta

PY - 2005/9/1

Y1 - 2005/9/1

N2 - 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 T2 and each bonding map is a surjective homomorphism), which admits three 4-sheeted covering maps f0: X0 → Y, f1: X1 → Y, f2: X2 → Y such that the total spaces and X0 = Y, X2 are pair-wise non-homeomorphic. Furthermore, Y admits a 2p-sheeted covering map f3: X3 → Y such that X3 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.

AB - 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 T2 and each bonding map is a surjective homomorphism), which admits three 4-sheeted covering maps f0: X0 → Y, f1: X1 → Y, f2: X2 → Y such that the total spaces and X0 = Y, X2 are pair-wise non-homeomorphic. Furthermore, Y admits a 2p-sheeted covering map f3: X3 → Y such that X3 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.

KW - Covering mapping

KW - Direct system

KW - H-connected space

KW - Inverse system

KW - p-adic number

KW - Quadratic number

KW - Torsion-free group of rank 2

KW - Torus-like continuum

UR - http://www.scopus.com/inward/record.url?scp=27644590199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27644590199&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2003.06.006

DO - 10.1016/j.topol.2003.06.006

M3 - Article

VL - 153

SP - 359

EP - 369

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 2-3 SPEC. ISS.

ER -