Arhangel'skiĭ sheaf amalgamations in topological groups

• Autorzy: Boaz Tsaban , Lyubomyr Zdomskyy
• Języki publikacji: 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.

Kategorie tematyczne

• 26A03: Foundations: limits and generalizations, elementary topology of the line
• 03E75: Applications of set theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 232
• Numer: 3
• Strony: 281-293

Daty

wydano

2016

Twórcy

autor

Boaz Tsaban

• Department of Mathematics, Bar-Ilan University, Ramat Gan 5290002, Israel
• Department of Mathematics, Weizmann Institute of Science, Rehovot 7610001, Israel

autor

Lyubomyr Zdomskyy

• Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Str. 25, 1090 Wien, Austria

Identyfikatory

DOI

10.4064/fm994-1-2016