楼: Originally posted by jollage at 2011-12-28 21:36:13:
对于某一个epsilon，总有n使
|x_n - y_{f(n)}|<|x_n - y_n| + |y_n - y_{f(n)}|< epsilon/2 + epsilon/2

|x_n - y_n|<epsilon/2  是已知，|y_n - y_{f(n)}|<epsilon/2 是紧空间。