On spaces that are l-equivalent to a disk

For a Tychonoff space X, Cp(X) denotes the space of all real-valued continuous functions on X with the pointwise convergent topology. Two Tychonoff spaces X and Y are said to be l-equivalent if Cp(X) and Cp(Y) are linearly homeomorphic. We give a characterization of spaces that are l-equivalent to a disk.