In [3] it was discovered that one of the main results in [1] (Theorem 5.2), applied to three spaces, contains a nontrivial gap in the argument, but neither the gap was closed nor a counterexample was provided. In [4] the authors verified that all three above mentioned applications of the theorem are true and stated a problem concerning the topological structure of one of these three spaces. In this paper we answer the problem and give a counterexample to the theorem in doubt. Also we establish a new way of constructing separable Hahn spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm182-1-5,
author = {Maria Zeltser},
title = {Sequences of 0's and 1's: sequence spaces with the separable Hahn property},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {87-98},
zbl = {1151.46003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm182-1-5}
}
Maria Zeltser. Sequences of 0's and 1's: sequence spaces with the separable Hahn property. Studia Mathematica, Tome 178 (2007) pp. 87-98. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm182-1-5/