A new version of the Semadeni derivative and functions on nonmetrizable rectangles

For $k \neq n$ let $K_1, \dotsc, K_n, L_1, \dotsc, L_k$ denote compact lines, so compact linearly ordered spaces. We study the problem whether there is a continuous linear embedding, surjection or isomorphism between Banach spaces $C(\prod_{i=1}^n K_i)$ and $C(\prod_{i=1}^k L_i)$. The answer is already known when considered compact lines are metrizable or separable. The goal of this talk is to give a characterisation which solves the problem for compact lines of uncountable character. We are using methods inspired by the papers of Semadeni and Candido.