# Arhangel'skiĭ sheaf amalgamations in topological groups

Boaz Tsaban; Lyubomyr Zdomskyy

Fundamenta Mathematicae (2016)

- Volume: 232, Issue: 3, page 281-293
- ISSN: 0016-2736

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topBoaz Tsaban, and Lyubomyr Zdomskyy. "Arhangel'skiĭ sheaf amalgamations in topological groups." Fundamenta Mathematicae 232.3 (2016): 281-293. <http://eudml.org/doc/283013>.

@article{BoazTsaban2016,

abstract = {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.},

author = {Boaz Tsaban, Lyubomyr Zdomskyy},

journal = {Fundamenta Mathematicae},

keywords = {amalgamation of convergent sequences; $\alpha $1space; $\alpha $1.5space; L-space},

language = {eng},

number = {3},

pages = {281-293},

title = {Arhangel'skiĭ sheaf amalgamations in topological groups},

url = {http://eudml.org/doc/283013},

volume = {232},

year = {2016},

}

TY - JOUR

AU - Boaz Tsaban

AU - Lyubomyr Zdomskyy

TI - Arhangel'skiĭ sheaf amalgamations in topological groups

JO - Fundamenta Mathematicae

PY - 2016

VL - 232

IS - 3

SP - 281

EP - 293

AB - 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.

LA - eng

KW - amalgamation of convergent sequences; $\alpha $1space; $\alpha $1.5space; L-space

UR - http://eudml.org/doc/283013

ER -

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