Geodesic
On hereditarily dentable sets in Banach spaces
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part IX, Tome 92 (1979), pp. 294-299

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The note deals with closed convex bounded hereditarily dentable sets in Banach spaces. As an example let us cite the following result: a closed convex bounded set $B$ is hereditarily dentable iff it is hereditarily $f$-dentable (i.e. $\forall K\subset B$, $\forall\varepsilon>0$, $\exists z\in K$: $z\not\in\mathrm{co} (K\setminus\{x\|x-z\|\le\varepsilon\}))$ and iff each closed subset of $B$ has an extreme point. The proof of the first equivalence (which is the main theorem of the paper) is based only on the definition of dentability and differs essen-tially from the Davis–Phelps proof for the special case $B=\{x:\|x\|\le1\}$. 
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     author = {O. I. Reinov},
     title = {On hereditarily dentable sets in {Banach} spaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {294--299},
     publisher = {mathdoc},
     volume = {92},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_92_a23/}
}
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O. I. Reinov. On hereditarily dentable sets in Banach spaces. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part IX, Tome 92 (1979), pp. 294-299. http://geodesic.mathdoc.fr/item/ZNSL_1979_92_a23/