Geodesic
On the set of zeros of a mapping of a cylinder
Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 6, Tome 167 (1988), pp. 159-163

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The author considers a continuous map $f\colon D^m\times D^k\to\mathbb{R}^m$ and determines a condition for the $C^\circ$-stability of a closed set $F\subset Z=f^{-1}(0)$. 
@article{ZNSL_1988_167_a11,
     author = {O. A. Ivanov},
     title = {On the set of zeros of a mapping of a cylinder},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {159--163},
     publisher = {mathdoc},
     volume = {167},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_167_a11/}
}
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O. A. Ivanov. On the set of zeros of a mapping of a cylinder. Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 6, Tome 167 (1988), pp. 159-163. http://geodesic.mathdoc.fr/item/ZNSL_1988_167_a11/