Index of notation for sets of continuous maps/Index

Index

1. $C(X,Y)$ - for topological spaces $(X,\mathcal{ J })$ and $(Y,\mathcal{ K })$, $C(X,Y)$ is the set of all continuous maps between them.
2. $C(I,X)$ - $I:\eq[0,1]\subset\mathbb{R}$, set of all paths on a topological space $(X,\mathcal{ J })$
   • Sometimes written: $C([0,1],X)$
3. $C(X,\mathbb{R})$ - The algebra of all real functionals on $X$. $\mathbb{R}$ considered with usual topology
   • See also: $C(X,\mathbb{K})$
4. $C(X,\mathbb{C})$ - The algebra of all complex functionals on $X$. $\mathbb{C}$ considered with usual topology
   • See also: $C(X,\mathbb{K})$
5. $C(X,\mathbb{K})$ - The algebra of all functionals on $X$, where $\mathbb{K}$ is either the reals, $\mathbb{R}$ or the complex numbers, $\mathbb{C}$, equipped with their usual topology.
6. $C(X,\mathbb{F})$ - structure unsure at time of writing - set of all continuous functions of the form $f:X\rightarrow\mathbb{F}$ where $\mathbb{F}$ is any field with an absolute value, with the topology that absolute value induces.