Thread: Affine space.

Let X be an affine space in F^n and let Y be an affine space in F^k. We look now on the next Cartesian product:

X x Y = {(x,y)| x in X, y in Y} c F^n x F^k =~F^(n+k)

Prove that if to think on X x Y as subset of F^(n+k) under the identification:

((x_1,...,x_n),(y_1,...,y_k)) =(x_1,...,x_n,y_1,...,y_k)

so we get an affine space.

Originally Posted by Also sprach Zarathustra

Let X be an affine space in F^n and let Y be an affine space in F^k. We look now on the next Cartesian product:

X x Y = {(x,y)| x in X, y in Y} c F^n x F^k =~F^(n+k)

Prove that if to think on X x Y as subset of F^(n+k) under the identification:

((x_1,...,x_n),(y_1,...,y_k)) =(x_1,...,x_n,y_1,...,y_k)

so we get an affine space.

What is your question here? what are ? are they simply subsets? remember that when you talk about affine space you're simply talking about for some without the usual vector space structure. Are you by any chance talking about algebraic subsets (zeroes of polynomials)? Please make a clear question!