- #1
simpleeyelid
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Continuously differentiable Function [tex]C^1
{}[/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
{}[/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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