- #1

VinnyCee

- 489

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(A) {f | f(0) = 0}

(B) {f | f(0) = 1}

(C) {f | f(0) = f(1)}

(D) [itex]C^0(R)[/itex] = {f | f is continous}

(E) [itex]C^1(R)[/itex] = {f | f is differentiable and f' is continous}

(F) P = {f | f is a polynomial}

(G) [itex]P_d\,\,\,\,=\,\,\,\,{f\,\in\,P\,|\,deg(f)\,\le\,d}[/itex]

(H) [itex]{f\,\in\,C^1(R)\,|\,f'\,=\,f}[/itex]

I have no idea what the last five of these instances mean. Case (C) is not a subspace because it only satifies the first rule that the set {0} be in the space before it can be considered a subspace, right?

Please help, I don't understand the terminology of the last five examples!