EDB — 0KB

[0KB] ¹ Let \((X, τ )\) and \((Y, σ)\) be two topological spaces, with \((Y, σ)\) Hausdorff.  ² Let \(E ⊆ X\) and \(f : E → Y\) . Let also \(x_ 0\) be an accumulation point of \(E\) in \(X\). We define that \(\lim _{x→x_ 0} f (x) = ℓ ∈ Y\) if and only if, for every neighborhood \(V\) of \(ℓ\) in \(Y\), there exists \(U\) neighbourhood of \(x_ 0\) in \(X\) such that \(f (U ∩ E ⧵ \{ x_ 0 \} ) ⊆ V\) .