Erratum to: Nonseparable closed vector subspaces of separable topological vector spaces (Monatshefte für Mathematik, (2017), 182, 1, (39-47), 10.1007/s00605-016-0876-2)

Jerzy Ka̧kol, Arkady G. Leiderman, Sidney A. Morris

Research output: Contribution to journalComment/debate

Abstract

All our formal Theorems, Propositions, Corollaries, Examples are correct. One of our main results is Theorem 2 Let I be an index set and Ei an lcs for each i ∈ I . If at least c of the Ei are not in D(ℝ), or equivalently do not have the weak topology, then the product Πi∈I Ei 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 Ec 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”.

Original languageEnglish
Pages (from-to)49-50
Number of pages2
JournalMonatshefte fur Mathematik
Volume182
Issue number1
DOIs
StatePublished - 1 Jan 2017

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