Continuity in GLUC

• Autores: Yevhen Zelenyuk
• Localización: Bulletin of the London Mathematical Society, ISSN 0024-6093, Vol. 46, Nº 5, 2014, págs. 981-988
• Idioma: inglés
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• Resumen

  • Given a locally compact group $G$, $G^{LUC}$ is the largest semigroup compactification of $G$ and $G^* =G^{LUC}\setminus G$. We show that (i) for every locally compact compactly generated Abelian group $G$ and for every $p,q\in G^* $, the multiplication in $G^{LUC}$ is discontinuous at $(p,q)$, (ii) there is a locally compact $\sigma$-compact torsion-free Abelian group $G$ for which, assuming Martin's Axiom, there are $p,q\in G^* $ such that the multiplication in $G^{LUC}$ is continuous at $(p,q)$, and (iii) it is consistent with ZFC that for every locally compact Abelian group $G$ and for every $p,q\in G^* $, the left translation by $p$ in $G^* $ is discontinuous at $q$