o-Boundedness of free objects over a Tychonoff space

Details o-Boundedness of free objects over a Tychonoff space o-Boundedness of free objects over a Tychonoff space

2005-09-26

arxiv.org/abs/math/0509607v1

Mathematics

General Topology

20 pages; Latex2e; Submitted to Matematychni Studii

Scientific paper

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.

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