Dear Colleagues,

I need the solution of the following problem:

Show that in a normed space $\displaystyle X$, vector addition and multiplication by scalars are continuous operations with respect to the norm; that is, the mappings defined by $\displaystyle (x,y)\longmapsto x+y$ and $\displaystyle (\alpha,x)\longmapsto \alpha x$ are continuous.

This problem in "Introductory Functional Analysis with applications, Erwin Kreyszig" problem 4 page 70.

Regards,

Raed.