[64] f(x)→b (x→a) ⇔ ∀ε＞0. ∃δ＞0. f(U(a,δ)∩D) ⊂ U(b,ε) ／ ∃lim f(x) (x→a) ⇒ f is bounded in some neighborhood of a in D.

https://www.evernote.com/shard/s29/sh/9860ca20-334f-4ace-a06b-18088739686a/d946b21aa1c8c0a051d32350191171ec