Geodesic
Problems of homeomorphism arising in the theory of grid generation
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 1, pp. 112-129

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Some general criteria of being a homeomorphism for continuous maps of topological spaces and topological manifolds are proved in this paper, as well as criteria of being a diffeomorphism for smooth maps of smooth manifolds. 
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     title = {Problems of homeomorphism arising in the theory of grid generation},
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M. F. Prokhorova. Problems of homeomorphism arising in the theory of grid generation. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 1, pp. 112-129. http://geodesic.mathdoc.fr/item/TIMM_2008_14_1_a9/