Question #2403

Consider the set of all functions [0,1] which are discontinuous. check if this set is a vector space over R with respect to pointwise addition and scalar multiplication

Expert's answer

It is necessary to verify axioms of a vector space.

The verification is direct.

For instance,

If f,g : [0,1]->R are two functions and T is a real number, then

& f+g& and T*f

are also a functions [0,1]->R.

The verification is direct.

For instance,

If f,g : [0,1]->R are two functions and T is a real number, then

& f+g& and T*f

are also a functions [0,1]->R.

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