An example of a non-topologizable algebra

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Authors ¹, ²

Institute of Mathematics, Polish Academy of Sciences, P.O. Box 137, 00-950 Warszawa, Poland
Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

We present an example of an algebra that is generated by

ω_{1}

elements, and cannot be made a topological algebra. This answers a problem posed by W. Żelazko.

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W. Żelazko, Example of an algebra which is non-topologizable as a locally convex algebra, Proc. Amer. Math. Soc. 110 (1990), 947-949.
W. Żelazko, On topologization of countably generated algebras, Studia Math. 112 (1994), 83-88.