# How to find Insomorphism

1. Aug 30, 2010

### sihaia

1. The problem statement, all variables and given/known data

(i) Set of all row vectors: (a1,....,an), aj in K; addition, multiplication defined componentwise. This space is denoted as Kn.
(ii) Set of all real valued functions f(x) defined on the real line, K = R.
(iii) Set of all functions with values in K, defined on an arbitrary set S.
(iv) Set of all polynomials of degree less than n with coefficients in K.

2. Relevant equations
1) Show that (i) and (iv) are isomorphic
2) Show that if S has n elements, (i) is the same as (iii)
3) Show that when K = R, (iv) is isomorphic with (iii) when S consists of n distinct points of R.

3. The attempt at a solution
I've solved 1), but I cannot solve others. I think that problem is that I don't understand definition of (iii).