I have to show that these examples below are (or not ) affine subspaces.I know what affine subspaces are but I have difficulties in applying what I studied
(1) S0(R) = {sequence $(s_n)$ in R such that $\lim_{n→∞} s_n = 1$};
according to me this is an affine subspace. I took one element of it , for example the sequence $s_n=1/n +1$, I have subtracted this sequence from all the others and this is a vector space because it contains a sequence made of 0. But I don't know now what its vector subspace should be, maybe $\lim_{ n→∞} s_n = 0$?
(2) Fx0,0([a,b],R)={f : [a, b] → R such that f(x0) = 0} (x0 ∈ [a, b] fixed);
This should be a vector space on its own so I think yes
(3) Fx0,1([a, b], R) = {f : [a, b] → R such that f(x0) = 1} (x0 ∈ [a, b] fixed)
another time if I take any element of it and subtract from all the remaining, I will obtain the example (2) so it is an affine subspace
(4) TK[T] = {polynomials p(T) ∈ K[T] with constant term =0};
it is a vector subspace s so it is also affine are my considerations right?
Thanks to everyone for your help!