My Math Notebook: [61] If B⊂A⊂R^n, f:A→R^m, and a ∈ the closure of B, then: f(x)→b (x→a, x∈B). ⇔ f(x_n)→b (n→∞) for any sequence (x_n) of points in B s.t. x_n→a (n→∞).

2011/10/28

[61] If B⊂A⊂R^n, f:A→R^m, and a ∈ the closure of B, then: f(x)→b (x→a, x∈B). ⇔ f(x_n)→b (n→∞) for any sequence (x_n) of points in B s.t. x_n→a (n→∞).

https://www.evernote.com/shard/s29/sh/5ba9c949-2df2-4904-849f-dcae40cccafd/596e2bb369518a726be0f5814d9e3b83