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”.
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The online version of the original article can be found under doi:10.1007/s00605-016-0876-2.
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Ka̧kol, J., Leiderman, A.G. & Morris, S.A. Erratum to: Nonseparable closed vector subspaces of separable topological vector spaces. Monatsh Math 182, 49–50 (2017). https://doi.org/10.1007/s00605-016-0943-8
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DOI: https://doi.org/10.1007/s00605-016-0943-8