Small bound isomorphisms of the domain of a closed *-derivation (Q1586736)

A generalization of the space \(C^{(1)}[0,1]\) of differentiable functions on \([0,1]\) is the domain \({\mathcal D}(\delta)4\) of a closed *-derivation in \(C(K)\), with \(K\) a compact Hausdorff space. The authors study in this context the following question posed by \textit{K. Jarosz} [Lectures Notes in Math. 1120 (1985; Zbl 0557.46029)]: ``Is there a positive \(\varepsilon\) such that for any compact subsets \(X,Y\) of real line and any linear isomorphism \(T:C^{(1)}(X)\rightarrow C^{(1)}(Y)\), \(\|T\|\|T^{-1}\|<\varepsilon\) implies that \(X\) and \(Y\) are homeomorphic?''.