A remark on non-existence of an algebra norm for the algebra of continuous functions on a topological space admitting an unbounded continuous function

Volume 116 / 1995

Alexander R. Pruss Studia Mathematica 116 (1995), 295-297 DOI: 10.4064/sm-116-3-295-297


Let X be any topological space, and let C(X) be the algebra of all continuous complex-valued functions on X. We prove a conjecture of Yood (1994) to the effect that if there exists an unbounded element of C(X) then C(X) cannot be made into a normed algebra.


  • Alexander R. Pruss

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