o-Boundedness of free objects over a Tychonoff space
General Topology
2007-05-23 v1
Abstract
In this paper we characterize [strict] o-boundedness of the free (abelian) topological group F(X) (A(X)) as well as the free locally-convex linear topological space L(X) in terms of properties of a Tychonoff space X. These properties appear to be close to so-called selection principles, which permits us to show, that (it is consistent with ZFC that) the property of Hurewicz (Menger) is l-invariant. This gives a method of construction of OF-undetermined topological groups with strong combinatorial properties.
Cite
@article{arxiv.math/0509607,
title = {o-Boundedness of free objects over a Tychonoff space},
author = {Lyubomyr Zdomskyy},
journal= {arXiv preprint arXiv:math/0509607},
year = {2007}
}
Comments
20 pages; Latex2e; Submitted to Matematychni Studii