Geodesic
A~non-compact closed sphere in a~constructive compact metric space
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part V, Tome 32 (1972), pp. 53-58

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Two examples of constructive (recursive) compact metric spaces containing non-compact closed spheres are described. 
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     author = {V. A. Lifshits and V. P. Chernov},
     title = {A~non-compact closed sphere in a~constructive compact metric space},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {53--58},
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     volume = {32},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1972_32_a7/}
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V. A. Lifshits; V. P. Chernov. A~non-compact closed sphere in a~constructive compact metric space. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part V, Tome 32 (1972), pp. 53-58. http://geodesic.mathdoc.fr/item/ZNSL_1972_32_a7/