Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9516807 | Topology and its Applications | 2005 | 11 Pages |
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 T2 and each bonding map is a surjective homomorphism), which admits three 4-sheeted covering maps f0:X0âY,f1:X1âY,f2:X2âY such that the total spaces X0=Y,X1 and X2 are pair-wise non-homeomorphic. Furthermore, Y admits a 2p-sheeted covering map f3:X3âY 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Katsuya Eda, JoÅ¡ko MandiÄ, Vlasta MatijeviÄ,