Geodesic
Topological properties of extreme points of convex compact sets in $\ell^2$
Sbornik. Mathematics, Tome 186 (1995) no. 3, pp. 327-336

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Under certain restrictions on given sets $M$ and $K$, where $M\subset K$ and $K$ is a metric compact set, a continuous map $\varepsilon\colon K\to\ell^2$ is constructed such that $\operatorname{ext}\operatorname{conv}\varepsilon(K)=\varepsilon(M)$ and the restriction of $\varepsilon$ to $M$ is a topological embedding. Here $\operatorname{ext}$ is the set of extreme points and $\operatorname{conv}$ is the closed convex hull. 
@article{SM_1995_186_3_a1,
     author = {E. M. Bronshtein},
     title = {Topological properties of extreme points of convex compact sets in $\ell^2$},
     journal = {Sbornik. Mathematics},
     pages = {327--336},
     publisher = {mathdoc},
     volume = {186},
     number = {3},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_3_a1/}
}
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E. M. Bronshtein. Topological properties of extreme points of convex compact sets in $\ell^2$. Sbornik. Mathematics, Tome 186 (1995) no. 3, pp. 327-336. http://geodesic.mathdoc.fr/item/SM_1995_186_3_a1/