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## Main Question or Discussion Point

My question is simple :

Suppose that [tex]f[/tex] is in [tex]C^\infty(U, [0,1])[/tex] where [tex]U[/tex] is an open of [tex]R^n[/tex] .

Is there [tex]g[/tex] in [tex]C^\infty(R^n,[0,1])[/tex] such that [tex]f=g[/tex] on [tex]U[/tex] ?

I would say yes, but I don't know how to prove it.

Thanks

Suppose that [tex]f[/tex] is in [tex]C^\infty(U, [0,1])[/tex] where [tex]U[/tex] is an open of [tex]R^n[/tex] .

Is there [tex]g[/tex] in [tex]C^\infty(R^n,[0,1])[/tex] such that [tex]f=g[/tex] on [tex]U[/tex] ?

I would say yes, but I don't know how to prove it.

Thanks