- #1
sihaia
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Homework Statement
(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.
Homework 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.
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).
Could someone please help me?