EDB — 13Y

[13Y] Let \((X,𝜏)\) be a topological space and \(f:X→ℝ\) a function; let \(\overline x∈ X\) be an accumulation point; let \(A\) be the set of all the limits \(\lim _ n f(x_ n)\) (when they exist) for all sequences \((x_ n)⊂ X\) such that \(x_ n→ \overline x\); then

moreover, if \((X,𝜏)\) satisfies the first axiom of countability, then equality holds and \(\inf A=\min A\).