Geodesic
Whitney maps for spaces of embedding hypersurfaces
Matematičeskie zametki, Tome 52 (1992) no. 3, pp. 117-122

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The existence of Whitney maps is proved, and it is also shown that if $X$ is a metrizable continuum, the Whitney map will be a trivial fibering with its own Hilbert cube. 
@article{MZM_1992_52_3_a12,
     author = {T. N. Radul},
     title = {Whitney maps for spaces of embedding hypersurfaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {117--122},
     publisher = {mathdoc},
     volume = {52},
     number = {3},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1992_52_3_a12/}
}
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T. N. Radul. Whitney maps for spaces of embedding hypersurfaces. Matematičeskie zametki, Tome 52 (1992) no. 3, pp. 117-122. http://geodesic.mathdoc.fr/item/MZM_1992_52_3_a12/