Geodesic
Subsets stable under a linear extension: local properties
Trudy Instituta matematiki, Tome 21 (2013) no. 2, pp. 142-153

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Subsets which are stable under a linear extension are considered. It is proved that any such subset is a vector subbundle over a neighborhood of the fixed point. 
@article{TIMB_2013_21_2_a8,
     author = {E. V. Pantsialeyeva},
     title = {Subsets stable under a linear extension: local properties},
     journal = {Trudy Instituta matematiki},
     pages = {142--153},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2013_21_2_a8/}
}
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E. V. Pantsialeyeva. Subsets stable under a linear extension: local properties. Trudy Instituta matematiki, Tome 21 (2013) no. 2, pp. 142-153. http://geodesic.mathdoc.fr/item/TIMB_2013_21_2_a8/