Can someone pls help me is for my study guide final?

In the first law of thermodynamics, triangle e=q-w, what does q stand for

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 radius of an atom is closest in size to a