Kaluza-Klein wormholes with the compactified fifth dimension

We consider wormhole solutions in five-dimensional Kaluza-Klein gravity in the presence of a massless ghost four-dimensional scalar field. The system possesses two types of topological nontriviality connected with the presence of the scalar field and of a magnetic charge. Mathematically, the presence of the charge appears in the fact that the S-3 part of a spacetime metric is the Hopf bundle S-3 -> S-2 with fiber S-1. We show that the fifth dimension spanned on the sphere S-1 is compactified in the sense that asymptotically, at large distances from the throat the size of SI is equal to some constant, the value of which can be chosen to lie, say, in the Planck region. Then, from the fourdimensional point of view, such a wormhole contains a radial magnetic (monopole) field, and an asymptotic four-dimensional observer sees a wormhole with the compactified fifth dimension.