We give a short proof of the following theorem of H. I. Levine [2]:
Let 𝒜 and ℬ be nonintersecting simple closed curves on an orientable surface S (compact or not).
(i) If 𝒜 is homotopic to zero, then 𝒜 bounds a closed disk in S.
(ii) If 𝒜 and ℬ are freely homotopic but not homotopic to zero then 𝒜∪ℬ bounds a closed cylinder in S.
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