Index of spaces

Using the index

People might use $i$ or $j$ or even $k$ for indicies, as such "numbers" are indexed as "num" (notice the lower-case) so a space like $C^k$ is under C_num.

We do subscripts first, so $A_i^2$ would be under $A_num_2$

Ordering

1. First come actual numbers.
2. Next come num terms.
3. Then come infty (which denotes $\infty$
4. Then come letters (upper case)
5. Then come brackets ( first, then [ then {

For example $C_0$ comes before $C_i$ comes before $C_\infty$ comes before $C_\text{text}$

Index

Space or name	Index	Context	Meaning
$C_k\text{ on }U$	C_num_ON	(Everywhere)	(SEE Classes of continuously differentiable functions) - a function is $C_k$ on $U$ if $U\subset\mathbb{R}^n$ is open and the partial derivatives of $f:U\rightarrow\mathbb{R}^m$ of all orders (up to and including $k$) are continuous on $U$
$C_k(U)$	C_num_(	(Everywhere)	(SEE Classes of continuously differentiable functions) - denotes a set, given $U\subseteq\mathbb{R}^n$ (that's open) $f\in C_k(U)$ if $f:U\rightarrow\mathbb{R}$ has continuous partial derivatives of all orders up to and including $k$ on $U$
$l_2$	L2	Functional Analysis	Space of square-summable sequences