An example of a non-topologizable algebra

• Autorzy: R. Frankiewicz , G. Plebanek
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46H05: General theory of topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995
• Tom: 116
• Numer: 1
• Strony: 85-87

Daty

wydano

1995

otrzymano

1995-03-09

poprawiono

1995-03-24

Twórcy

autor

R. Frankiewicz

• Institute of Mathematics, Polish Academy of Sciences, P.O. Box 137, 00-950 Warszawa, Poland

autor

G. Plebanek

• Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• [1] R. Frankiewicz and P. Zbierski, Hausdorff Gaps and Limits, North-Holland, Amsterdam, 1994.
• [2] V. Müller, On topologizable algebras, Studia Math. 99 (1991), 149-153.
• [3] W. Żelazko, Selected Topics in Topological Algebras, Aarhus Univ. Lecture Notes 31, 1971.
• [4] W. Żelazko, Example of an algebra which is non-topologizable as a locally convex algebra, Proc. Amer. Math. Soc. 110 (1990), 947-949.
• [5] W. Żelazko, On topologization of countably generated algebras, Studia Math. 112 (1994), 83-88.