Index of spaces

Using the index

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

We do subscripts first, so [ilmath]A_i^2[/ilmath] would be under [ilmath]A_num_2[/ilmath]

Ordering

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

For example [ilmath]C_0[/ilmath] comes before [ilmath]C_i[/ilmath] comes before [ilmath]C_\infty[/ilmath] comes before [ilmath]C_\text{text} [/ilmath]

Index

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