EDB — 1NY

[1NY]Let \(A⊆ ℝ^ n\) be open and let \(f:A→ℝ\) be a function. Show that \(f\) is continuous if and only if, for each curve \(𝛾:[0,1]→ A\) we have that \(f◦ 𝛾\) is continuous.