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

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U2 - 10.1016/j.topol.2003.06.006

DO - 10.1016/j.topol.2003.06.006

M3 - Article

AN - SCOPUS:27644590199

SN - 0166-8641

VL - 153

SP - 359

EP - 369

JO - Topology and its Applications

JF - Topology and its Applications

IS - 2-3 SPEC. ISS.

ER -