TY - JOUR

T1 - Erratum to

T2 - Nonseparable closed vector subspaces of separable topological vector spaces (Monatshefte für Mathematik, (2017), 182, 1, (39-47), 10.1007/s00605-016-0876-2)

AU - Ka̧kol, Jerzy

AU - Leiderman, Arkady G.

AU - Morris, Sidney A.

N1 - Publisher Copyright:
© 2016, Springer-Verlag Wien.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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”.

AB - 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”.

UR - http://www.scopus.com/inward/record.url?scp=84976320944&partnerID=8YFLogxK

U2 - 10.1007/s00605-016-0943-8

DO - 10.1007/s00605-016-0943-8

M3 - Comment/debate

AN - SCOPUS:84976320944

VL - 182

SP - 49

EP - 50

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 1

ER -