Nearly disjoint sequences in convergence $l$-groups

Jakubík, Ján. "Nearly disjoint sequences in convergence $l$-groups." Mathematica Bohemica 125.2 (2000): 139-144. <http://eudml.org/doc/248662>.

@article{Jakubík2000,
abstract = {For an abelian lattice ordered group $G$ let $G$ be the system of all compatible convergences on $G$; this system is a meet semilattice but in general it fails to be a lattice. Let $\alpha _\{nd\}$ be the convergence on $G$ which is generated by the set of all nearly disjoint sequences in $G$, and let $\alpha $ be any element of $G$. In the present paper we prove that the join $\alpha _\{nd\}\vee \alpha $ does exist in $G$.},
author = {Jakubík, Ján},
journal = {Mathematica Bohemica},
keywords = {nearly disjoint sequence; strong convergence; convergence $\ell $-group; convergence -group; nearly disjoint sequence; strong convergence},
language = {eng},
number = {2},
pages = {139-144},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Nearly disjoint sequences in convergence $l$-groups},
url = {http://eudml.org/doc/248662},
volume = {125},
year = {2000},
}

TY - JOUR
AU - Jakubík, Ján
TI - Nearly disjoint sequences in convergence $l$-groups
JO - Mathematica Bohemica
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 125
IS - 2
SP - 139
EP - 144
AB - For an abelian lattice ordered group $G$ let $G$ be the system of all compatible convergences on $G$; this system is a meet semilattice but in general it fails to be a lattice. Let $\alpha _{nd}$ be the convergence on $G$ which is generated by the set of all nearly disjoint sequences in $G$, and let $\alpha $ be any element of $G$. In the present paper we prove that the join $\alpha _{nd}\vee \alpha $ does exist in $G$.
LA - eng
KW - nearly disjoint sequence; strong convergence; convergence $\ell $-group; convergence -group; nearly disjoint sequence; strong convergence
UR - http://eudml.org/doc/248662
ER -