Examples of Nondistinguished Function Spaces C _p (X)

In the pointwise topology, familiar function spaces

,

C_{p}(\mathbb{R}) C p ( R )

,

C_{p}\left[ 0,1\right] C p [ 0 , 1 ]

, and

C_{p}(\text{Cantor set}) C p ( Cantor set )

are not distinguished.