Arhangel'skiĭ sheaf amalgamations in topological groups

Boaz 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 -