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Let [tex]C([0,1])[/tex] be the collection of all complex-valued continuous functions on [tex][0,1][/tex].
Define [tex]d(f,g)=\int\limits_0^{1}\frac{|f(x)-g(x)|}{1+|f(x)-g(x)|}dx[/tex] for all [tex]f,g \in C([0,1])[/tex]
[tex]C([0,1])[/tex] is an invariant metric space.
Prove that [tex]C([0,1])[/tex] is a topological vector space
Define [tex]d(f,g)=\int\limits_0^{1}\frac{|f(x)-g(x)|}{1+|f(x)-g(x)|}dx[/tex] for all [tex]f,g \in C([0,1])[/tex]
[tex]C([0,1])[/tex] is an invariant metric space.
Prove that [tex]C([0,1])[/tex] is a topological vector space