Geodesic
On some conditions on mappings of spaces onto cylindrical domains
Matematičeskie zametki, Tome 11 (1972) no. 4, pp. 459-462

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Criteria are given for a local homeomorphism $f: R^n\to R^n$ to be a homeomorphism of $R^n$ onto a strip. In the planar case, this gives a condition for $f$ to be a transformation of $R^2$ onto a band. 
@article{MZM_1972_11_4_a12,
     author = {V. A. Zorich and V. S. Samovol},
     title = {On some conditions on mappings of spaces onto cylindrical domains},
     journal = {Matemati\v{c}eskie zametki},
     pages = {459--462},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_4_a12/}
}
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V. A. Zorich; V. S. Samovol. On some conditions on mappings of spaces onto cylindrical domains. Matematičeskie zametki, Tome 11 (1972) no. 4, pp. 459-462. http://geodesic.mathdoc.fr/item/MZM_1972_11_4_a12/