The absence of bases from certain separable linear topological spaces

We give examples of separable linear topological spaces without Shauder-type bases. We prove that every linear set X of dimension ₀ 2²₀ can be provided with a separable locally convex topology for which there is no Shauder-type basis.Translated from Matematicheskie Zametki, Vol. 12, No. 5, pp. 583–589, November, 1972.In conclusion the author wishes to express his gratitude to M. M. Dragilev for his attention to the paper.