For every Hausdorff space \(Y\) there exists a non-trivial Moore space on which all continuous functions into \(Y\) are constant
In an early version of a recent survey article on categorical topology, H. Herrlich raised the question whether there exists a Moore space \(Y\) such that every Moore space can be embedded into some topological power of \(Y\). We answer this question by proving the result mentioned in the title, which shows that there does not exist any Hausdorff space \(Y\) with the property that every Moore space can be embedded into some power of \(Y\). Additionally, a simple proof is given of the theorem of H. Herrlich and A. Ramer that for every \(T_ 1\)-space \(X\) there exists a regular space \(S\) containing two distinct points \(a, b\) such that \(f(a)=f(b)\) for every continuous mapping from \(S\) into \(X\).
scientific article; zbMATH DE number 3855968