更改

In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it on the floor, and flattening it. In some places the flat string will cross itself in an approximate "X" shape. The points on the floor where it does this are one kind of singularity Perhaps the string will also touch itself without crossing, like an underlined "<u>U</u>". This is another kind of singularity. Unlike the double point, it is not stable, in the sense that a small push will lift the bottom of the "U" away from the "underline".

In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it on the floor, and flattening it. In some places the flat string will cross itself in an approximate "X" shape. The points on the floor where it does this are one kind of singularity Perhaps the string will also touch itself without crossing, like an underlined "<u>U</u>". This is another kind of singularity. Unlike the double point, it is not stable, in the sense that a small push will lift the bottom of the "U" away from the "underline".

在数学中，奇点理论研究的空间几乎是流形，但不完全是流形。如果忽略弦的厚度，弦可以作为一维流形的例子。一个奇点的形成可以通过把它团起来，扔在地板上，然后把它压扁。完成以上步骤即可得到一个奇点。在某些地方，扁平的字符串会以近似“ x”的形状交叉自身。这些扔在地板上的点是一种奇点。也许字符串也会在没有交叉的情况下接触自己，就像u的下划线那样。这是另一种奇点。与双点不同，它是不稳定的，在某种意义上说，一个小的推动将提升底部的“ u”远离“下划线”。

在数学中，奇点理论研究的空间几乎都是流形，但不完全是流形。如果忽略弦的厚度，弦可以作为一维流形的例子。一个奇点的形成可以通过把它团起来，扔在地板上，然后把它压扁。完成以上步骤即可得到一个奇点。在某些地方，扁平的字符串会以近似“ x”的形状交叉自身。这些扔在地板上的点是一种奇点。也许字符串也会在没有交叉的情况下接触自己，就像u的下划线那样。这是另一种奇点。与双点不同，它是不稳定的，在某种意义上说，一个小的推动将提升底部的“ u”远离“下划线”。