[求助] 求助大神：C_0在C交L无穷里稠密吗？应该怎么证明？

4楼: Originally posted by hank612 at 2013-10-10 12:38:46
how about the definition of metric?

If use the Sup_x |f(x)-g(x)| for the distance, then the constant x=1 cannot be approximated by any finite-supported continuous function.

If use Integral( | ...

2楼: Originally posted by hank612 at 2013-10-10 03:46:59
你能说说函数空间的度量是如何定义的吗? 还有, C 空间的定义是什么, 你想要比较的两个空间谁大谁小, 我怎么觉得 C交 L^{Infinity}更小呢?

3楼: Originally posted by 荞桥 at 2013-10-10 08:13:10
\omega是有界开集，C_0(\omega)是连续有紧支集的，C(\omega)是连续，L无穷\omega是有界，C_0当然是连续有界的...