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o-Boundedness of free objects over a Tychonoff space

Research paper by Lyubomyr Zdomskyy

Indexed on: 26 Sep '05Published on: 26 Sep '05Published in: Mathematics - General Topology



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.