Finite products of connected nowhere separable linearly ordered spaces (Q2049881)

A topological space is nowhere separable if it does not have a nonempty open subspace that is separable. In this paper, the author proves the following main result: Let \(n\) be any positive integer and \(K_1, \dots , K_{n}, L_1, \dots , L_{n}\) be connected nowhere separable linearly ordered spaces. Then for any continuous injective function \(f : \prod_{i\le n}K_i \rightarrow \prod_{i\le n}L_i\), there is a bijection \(h : \{1, 2, \dots, n\} \rightarrow \{1, 2, \dots, n\}\) and a function \(\tau_{i} : K_{i} \rightarrow L_{h(i)}\) for each \(i \le n\) such that for all \(x\in \prod_{i\le n}K_i\), \(f(x)(h(i)) = \tau_{i}(x(i))\) holds for every \(i\le n\). This result generalizes results obtained earlier by the author for the case \(n=2\) [\textit{T. Ishiu}, Topol. Proc. 50, 319--333 (2017; Zbl 1479.54026)].