我們證明了平面上的四頂點定理能夠被推廣到任意簡單連通的二維非負常曲率流形上。另一方面，在特定形式的非簡單連通流形上，我們給出四頂點定理無法被推廣的反例。

We show that the Four-Vertex Theorem can be extended on any two-dimensional simply connected space form with non-negative sectional curvature. On the other hand, we give counterexamples to show that the Four-Vertex Theorem can not be extended on a type of non-simply connected space form.

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