2.6 Important Sets of Functions

Types: N/A
Examples: N/A
Constructions: N/A
Generalizations: 1.1 Set, 2.5 Function (Set Theory)

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Important Sets of Functions

Let $I \subseteq R$ . Then,

\begin{aligned} P_{n} (I) & = {f : f : I \to R and f is a polynomial with deg (f) \leq n for n \in N} . \\ C^{(\infty)} (I) & = {f : f : I \to R and f has continuous derivatives of all orders on I} . \\ C^{(p)} (I) & = {f : f : I \to R and f has continous p th derivative for p \in N on I} . \\ C^{(1)} (I) & = {f : f : I \to R and f has a continous first derivative on I} . \\ C (I) & = {f : f : I \to R and f is a continous on I} . \\ F (I) & = {f : f : I \to R} . \end{aligned}