Arhangel'skiѤ sheaf amalgamations in topological groups

Boaz Tsaban, Lyubomyr Zdomskyy

Research output: Contribution to journalArticlepeer-review

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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 α1.5 is equivalent to Arhangel'skiѤ'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 Cp(X) of continuous real-valued functions on X with the topology of pointwise convergence has Arhangel'skiѤ's property α1 but is not countably tight. This follows from results of Arhangel'skiѤ-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.

Original languageEnglish
Pages (from-to)281-293
Number of pages13
JournalFundamenta Mathematicae
Issue number3
StatePublished - 2016

Bibliographical note

Publisher Copyright:
© 2016 Instytut Matematyczny PAN.


  • Amalgamation of convergent sequences
  • L-space
  • α space
  • α space


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