Question

Each of the following defines a metric space X which is a subset of R^2 with...

Each of the following defines a metric space X which is a subset of R^2 with the Euclidean metric, together with a subset E ⊂ X. For each,

1. Find all interior points of E,

2. Find all limit points of E,

3. Is E is open relative to X?,

4. E is closed relative to X?

I don't worry about proofs just answers is fine!

a) X = R^2, E = {(x,y) ∈R^2 : x^2 + y^2 = 1, y > 0}.

b) X = {(x,y) ∈R^2 : x^2 + y^2 = 1}, E = {(x,y) ∈ X : x^2 + y^2 = 1, y > 0}.

c) X = {(n,0) ∈R^2 : n ∈N}, E = {(2n,0) ∈R^2 : n ∈N}.

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