Geodesic
The minimization property for spaces that are normed over semifields
Matematičeskie zametki, Tome 5 (1969) no. 3, pp. 297-304 Cet article a éte moissonné depuis la source Math-Net.Ru

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We show that if each nonempty subset of a space $X$, normed over a pair of topological semifields, has the minimization property, then $X$ is a real normed space (up to an isomorphism). 
@article{MZM_1969_5_3_a2,
     author = {A. I. Vasil'ev},
     title = {The minimization property for spaces that are normed over semifields},
     journal = {Matemati\v{c}eskie zametki},
     pages = {297--304},
     year = {1969},
     volume = {5},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_3_a2/}
}
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A. I. Vasil'ev. The minimization property for spaces that are normed over semifields. Matematičeskie zametki, Tome 5 (1969) no. 3, pp. 297-304. http://geodesic.mathdoc.fr/item/MZM_1969_5_3_a2/