Continuously differentiable Function [tex]C^1(adsbygoogle = window.adsbygoogle || []).push({});

{}[/tex] [tex]\left[0,1\right][/tex] is complete with respect to the metric space

[tex]D_\infty{}[/tex]{f,g}=sup{[tex]\left|f(t)-g(t)\right|[/tex]}+sup{[tex]\left|f^1{}(t)-g^1{}(t)\right|[/tex]}

but not in the [tex]d_\infty{}[/tex]{f,g}=sup{[tex]\left|f(t)-g(t)\right|[/tex]}

Thanks for the helps in advance.

Regards...

BI

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# A question of the complete metric space!

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