Evaluate the following statement and explain why it is either true or false: if a spacecraft could travel fast enough, it could reach the celestial sphere in about a month.

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Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k

The star nearest to our sun is proxima centauri, at a distance of 4.3 light-years from the sun. how far away, in km, is proxima centauri from the sun?