V is a vector space of all continous function from R to R If

V is a vector space of all continous function from R to R

If V is a vector space and V* is the dual space with the addition, check that the addition is commutative

Solution

V* is the dual space with addition, V is vector space .

Given any vector space V over a field F, the dual space V is defined as the set of all linear maps : V F (linear functionals). The dual space V itself becomes a vector space over F when equipped with an addition and scalar multiplication satisfying commutative relation.. So, yes the addition is commutative.