Almost periodic compactifications of group extensions

Junghenn, H. D., and Milnes, Paul. "Almost periodic compactifications of group extensions." Czechoslovak Mathematical Journal 52.2 (2002): 237-254. <http://eudml.org/doc/30696>.

@article{Junghenn2002,
abstract = {Let $N$ and $K$ be groups and let $G$ be an extension of $N$ by $K$. Given a property $\mathcal \{P\}$ of group compactifications, one can ask whether there exist compactifications $N^\{\prime \}$ and $K^\{\prime \}$ of $N$ and $K$ such that the universal $\mathcal \{P\}$-compactification of $G$ is canonically isomorphic to an extension of $N^\{\prime \}$ by $K^\{\prime \}$. We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties $\mathcal \{P\}$ and then apply this result to the almost periodic and weakly almost periodic compactifications of $G$.},
author = {Junghenn, H. D., Milnes, Paul},
journal = {Czechoslovak Mathematical Journal},
keywords = {group extension; semidirect product; topological group; semitopological semigroup; right topological semigroup; compactification; almost periodic; weakly almost periodic; strongly almost periodic; group extension; semidirect product; topological group; compactification; almost periodic},
language = {eng},
number = {2},
pages = {237-254},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Almost periodic compactifications of group extensions},
url = {http://eudml.org/doc/30696},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Junghenn, H. D.
AU - Milnes, Paul
TI - Almost periodic compactifications of group extensions
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 2
SP - 237
EP - 254
AB - Let $N$ and $K$ be groups and let $G$ be an extension of $N$ by $K$. Given a property $\mathcal {P}$ of group compactifications, one can ask whether there exist compactifications $N^{\prime }$ and $K^{\prime }$ of $N$ and $K$ such that the universal $\mathcal {P}$-compactification of $G$ is canonically isomorphic to an extension of $N^{\prime }$ by $K^{\prime }$. We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties $\mathcal {P}$ and then apply this result to the almost periodic and weakly almost periodic compactifications of $G$.
LA - eng
KW - group extension; semidirect product; topological group; semitopological semigroup; right topological semigroup; compactification; almost periodic; weakly almost periodic; strongly almost periodic; group extension; semidirect product; topological group; compactification; almost periodic
UR - http://eudml.org/doc/30696
ER -