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o-Boundedness of free objects over a Tychonoff space

2005/09/26 by Lyubomyr Zdomskyy, Zdomskyy, Lyubomyr
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Mathematical and Theoretical Analysis #math.GN

paper · pdf · doi:10.48550/arxiv.math/0509607

20 pages; Latex2e; Submitted to Matematychni Studii

arxiv created 2005/09/26 · openalex publication_date 2005/09/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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