a question on notation for function spaces 
If $X$ is some topological space, such
  as the unit interval $[0,1]$, we can
  consider the space of all continuous
  functions from $X$ to $R$. This is a
  vector subspace of $R^X$ since the sum
  of any two continuous functions is
  continuous and scalar multiplication
  is continuous.

Please let me know the notation $R^X$ in the above example.

This means the space of all functions from $X$ to $R$. Without regard for any structure. Set-theoretic ones.
