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A finite-to-one criterion for covering maps. (English. Russian original) Zbl 0558.54011
Sov. Math., Dokl. 28, 587-590 (1983); translation from Dokl. Akad. Nauk SSSR 273, 54-58 (1983).
The author characterizes finite-to-one covering maps within the class of local homeomorphisms of Hausdorff spaces satisfying some other conditions; he gives, among others, sufficient conditions under which a precisely m-fold covering map of a compact subset Q of a Hausdorff space has an extension onto an open neighbourhood of Q which is also a precisely covering map. In the case of domains in Banach spaces he obtains conditions sufficient for a map to be a precisely m-fold covering map.
Reviewer: J Chvalina

MSC:
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
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