Note on function spaces with the topology of pointwise convergence
The paper contains two examples of function spaces \(C_p(X)\) of continuous real-valued functions together with the topology of pointwise convergence. The first example is the Cook continuum. The author proves that for any Cook continuum \(M\) the space \(C_p(M)^n\) is uniformly homeomorphic to \(C_p(M)^m\) if and only if \(n=m\). The second example provides a negative answer to Problem 45 of [\textit{A. V. Arkhangel'skij}, Hvsek, M. (ed.) et al., Recent progress in general topology, Amsterdam: North Holland, 1--56 (1992; Zbl 0814.54009)].
scientific article; zbMATH DE number 2004965