Geodesic
The absence of bases from certain separable linear topological spaces
Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 583-589.

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We give examples of separable linear topological spaces without Shauder-type bases. We prove that every linear set $X$ of dimension $\aleph_0 \dim X\leqslant2^2\aleph_0$ can be provided with a separable locally convex topology for which there is no Shauder-type basis. 
@article{MZM_1972_12_5_a11,
     author = {V. P. Kondakov},
     title = {The absence of bases from certain separable linear topological spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {583--589},
     publisher = {mathdoc},
     volume = {12},
     number = {5},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a11/}
}
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V. P. Kondakov. The absence of bases from certain separable linear topological spaces. Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 583-589. http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a11/