f,g are uniformly continuous on [a,b]

any example f*g which is not uniformly continuous.

and :

example, f,g are bounded but fg is uniformly continuous.

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- Oct 20th 2008, 12:43 PMszpengchaoany example of product of two uniformly continuous functions
f,g are uniformly continuous on [a,b]

any example f*g which is not uniformly continuous.

and :

example, f,g are bounded but fg is uniformly continuous. - Oct 20th 2008, 12:50 PMLaurent
Is this what you meant to write?

Anyway, if you're looking for functions $\displaystyle f,g$ on $\displaystyle [a,b]$ that are uniformly continuous and such that their product is not, you won't find any. Indeed, on a segment, uniformly continuous is equivalent to continuous (this is called Heine Theorem (at least in France)), and the product of two continuous functions is continuous. - Oct 20th 2008, 12:51 PMszpengchaowrong
- Oct 20th 2008, 01:13 PMLaurent