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Consider Rn with the usual topology for n = 1, 2, 3. Each of the following options gives topological spaces X and Y with respective induced topologies. In which option is X home-omorphic to Y ?

(A) X = {(x, y, z) ∈ R^3: x^2 + y^2 = 1}, Y = {(x, y, z) ∈ R^3: z = 0, x^2 + y^2 != 0}
(B) X = {(x, y) ∈ R^2: y = sin(1/x), 0 < x ≤ 1}∪{(x, y) ∈ R^2: x = 0, −1 ≤ y ≤ 1}, Y = [0, 1] ⊆ R
(C) X = {(x, y) ∈ R^2: y = x sin(1/x), 0 < x ≤ 1}, Y = [0, 1] ⊆ R
(D) X = {(x, y, z) ∈ R^3: x^2 + y^2 = 1}, Y = {(x, y, z) ∈ R^3: x^2 + y^2 = z^2 != 0}

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