- #1

- 12

- 0

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

Last edited: