Arhangel'skiĭ sheaf amalgamations in topological groups
Boaz Tsaban, Lyubomyr Zdomskyy (2016)
Fundamenta Mathematicae
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We consider amalgamation properties of convergent sequences in topological groups and topological vector spaces. The main result of this paper is that, for arbitrary topological groups, Nyikos’s property is equivalent to Arhangel’skiĭ’s formally stronger property α₁. This result solves a problem of Shakhmatov (2002), and its proof uses a new perturbation argument. We also prove that there is a topological space X such that the space of continuous real-valued functions on X with the...