Torus-like continua which are not self-covering spaces

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 X0=Y,X1 and 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.