$\displaystyle f_{n}$ converges uniformly to f $\displaystyle g_{n}$ converges uniformly to g show that pointwise product $\displaystyle g_{n}f_{n}$ does not converge uniformly to gf
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fn=gn=x+1/n should work I think
i dont think it works, if u try to draw its graph, it converges to fg!
Last edited by szpengchao; Oct 19th 2008 at 12:58 PM.
yes, pointwise... not uniformly.
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