simply connected surface的意思|示意

Any object with a simply connected surface can be smoothed out to look like a sphere.

任何具有单连通表面的物体都能简化成一个球体。

In this example, the surface is not simply connected and any smoothed-out object looks like a torus with at least one hole.

在这个例子里，圈饼表面就是非单连通的，并且这类物体的简化就会像是至少有一个洞的曲面。

OK, so that's the definition of the surface of a sphere being simply connected.

这就是球面上，对单连通的定义。

With the help of them, it can be proved that the non-simply connected compact surface with nonnegative curvature must be flat.

讨论了紧致非单连通的具非负曲率的流形的一些几何性质，并应用它们证明了具非负曲率的紧致非单连通曲面必为平坦的。