1 Erratum to: Monatsh Math DOI 10.1007/s00605-016-0876-2

All our formal Theorems, Propositions, Corollaries, Examples are correct. One of our main results is

Theorem 2

Let I be an index set and \(E_i\) an lcs for each \(i\in I\). If at least \(\mathfrak {c}\) of the \(E_i\) are not in \(\mathfrak {V}(\mathbb R),\) or equivalently do not have the weak topology,  then the product \(\prod _{i\in I}E_i\) has a nonseparable closed vector subspace.

However,  some statements in the Abstract and elsewhere claim too much.

Thanks to e-mail from Stephen A. Saxon,  we realized that the product \(E^{\mathfrak {c}}\) may have a nonseparable closed vector subspace even when lcs E has the weak topology. Take E to be the lcs of our Example 1; then this E has the weak topology, is separable and contains a nonseparable closed vector subspace. Our erroneous claim appears after Problem 2, after Theorem 2, and in the Abstract. In particular,  we have not given a complete answer to Problem 2.

Also,  in the last sentence of the fifth paragraph of the Introduction,  “a compact X” should be replaced by “a separable compact X”.