Special vector spaces

Here is a list of special vector spaces

W.r.t function support
There are two special vector spaces w.r.t. support.
 * $$C_c(\mathbb{R})$$, the space of all continuous functions with compact support: $$C_c(\mathbb{R}):=\left\{f:\mathbb{R}\to\mathbb{C} : f \text{is continuous and has compact support}\right\}$$
 * $$C_0(\mathbb{R})$$, the space of all continuous functions that tend to zero as $$x\to\pm\infty$$: $$C_0(\mathbb{R}):=\left\{f:\mathbb{R}\to\mathbb{C} : f \text{is continuous and } f(x)\to 0 \text{ as } x\to\pm\infty\right\}$$

Some Banach Spaces

 * $$L^p(\mathbb{R})$$