Geodesic
Reduction to general position of a mapping of a one-dimensional polyhedron, depending continuously on a parameter
Izvestiya. Mathematics, Tome 27 (1986) no. 2, pp. 359-389 
S. I. Yablokova. Reduction to general position of a mapping of a one-dimensional polyhedron, depending continuously on a parameter. Izvestiya. Mathematics, Tome 27 (1986) no. 2, pp. 359-389. http://geodesic.mathdoc.fr/item/IM2_1986_27_2_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is devoted to a proof of the fact that by refining the triangulation of a one-dimensional polyhedron, one can approximate a given mapping of that polyhedron into $\mathbf R^k$ by a piecewise linear mapping having no more than a zero-dimensional violation of general position; and that all this can be carried out continuously with respect to a parameter running through a strongly paracompact space. Spaces of triangulations of one-dimensional simplexes are also investigated, and the structure of spaces of semilinear mappings of a one-dimensional polyhedron into Euclidean space is considered. Figures: 6. Bibliography: 6 titles.

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