Geodesic
Bounded compactness of sets in linear metric spaces
Matematičeskie zametki, Tome 11 (1972) no. 6, pp. 651-660

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An analog of the well known concept of bounded compactness from the theory of normed spaces is investigated in a linear metric space $X$. From the results obtained follows, for example, a sufficient condition for approximative compactness of a finite-dimensional subspace $L\subset X$. 
@article{MZM_1972_11_6_a5,
     author = {A. I. Vasil'ev},
     title = {Bounded compactness of sets in linear metric spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {651--660},
     publisher = {mathdoc},
     volume = {11},
     number = {6},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_6_a5/}
}
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A. I. Vasil'ev. Bounded compactness of sets in linear metric spaces. Matematičeskie zametki, Tome 11 (1972) no. 6, pp. 651-660. http://geodesic.mathdoc.fr/item/MZM_1972_11_6_a5/