如果知道了，向量空间在单连通区域内处处有定义，那么就可以毫无顾忌地，在这个区域里使用格林公式了？
Well, if you know that your vector field is defined everywhere in a simply connected region, then you don't have to worry about this question of, can I apply Green's theorem to the inside?
全空间去掉原点，它是单连通的吗？
OK, so space with the origin removed, OK, you think it's simply connected?
他在1904年就提出猜想：在四维空间，所有单连通的封闭三维面都能转化为一个三维球体。
His conjecture, made in 1904, was that in this four-dimensional world, all closed three-dimensional surfaces that are simply connected could be transformed to look like a three-dimensional sphere.
因为我已经告诉过你们空间是单连通的，所以，如果我们真的想要运用Stokes定理，那么我总是可以把它运用于任何曲线，我应该做什么呢？
So, if we really wanted to apply Stokes theorem, because I've been telling you that space is simply connected, and I will always be able to apply Stokes theorem to any curve, what would I do?
单连通和非单连通的概念，研究哪些环路能界定曲面，可以用来对空间内部物体的形状进行分类。
This concept of being simply connected or not, and studying which loops bound surfaces or not can be used to classify shapes of things inside space.
文中还定义了平面单连通多边形区域的所谓分层三角剖分，并确定了此剖分下二次样条空间的维数。
Then, a new kind of so-called stratified triangulation of a simply connected planar polygonal region is introduced.
文中还定义了平面单连通多边形区域的所谓分层三角剖分，并确定了此剖分下二次样条空间的维数。
Then, a new kind of so-called stratified triangulation of a simply connected planar polygonal region is introduced.
应用推荐