The absence of bases from certain separable linear topological spaces

V. P. Kondakov

Rostov State University

Abstract: 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.

UDC: 513.88

Received: 23.02.1971

 English version: Mathematical Notes, 1972, 12:5, 787–790

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