Geodesic
Remarkable Hyperplanes in Locally Convex Spaces of Dimension at Most C
Canadian mathematical bulletin, Tome 24 (1981) no. 3, pp. 369-371

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DOI

Every locally convex space E of dimension at most c contains a hyperplane G with the following property: the linear hull of each bounded Banach disk in G is finite-dimensional. 
Tsirulnikov, Bella. Remarkable Hyperplanes in Locally Convex Spaces of Dimension at Most C. Canadian mathematical bulletin, Tome 24 (1981) no. 3, pp. 369-371. doi: 10.4153/CMB-1981-056-7
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     author = {Tsirulnikov, Bella},
     title = {Remarkable {Hyperplanes} in {Locally} {Convex} {Spaces} of {Dimension} at {Most} {C}},
     journal = {Canadian mathematical bulletin},
     pages = {369--371},
     year = {1981},
     volume = {24},
     number = {3},
     doi = {10.4153/CMB-1981-056-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-056-7/}
}
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