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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2016 | 232 | 3 | 281-293

## Arhangel'skiĭ sheaf amalgamations in topological groups

EN

### Abstrakty

EN
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 $α_{1.5}$ 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 $C_{p}(X)$ of continuous real-valued functions on X with the topology of pointwise convergence has Arhangel'skiĭ's property α₁ but is not countably tight. This follows from results of Arhangel'skiĭ-Pytkeev, Moore and Todorčević, and provides a new solution, with stronger properties than the earlier solution, of a problem of Averbukh and Smolyanov (1968) concerning topological vector spaces.

281-293

wydano
2016

### Twórcy

autor
• Department of Mathematics, Bar-Ilan University, Ramat Gan 5290002, Israel
• Department of Mathematics, Weizmann Institute of Science, Rehovot 7610001, Israel
autor
• Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Str. 25, 1090 Wien, Austria