Natural topologies on Colombeau algebras

Abstract

We define intrinsic, natural and metrizable topologies
${\mathcal T}_{\Omega}$, ${\mathcal T}$, ${\mathcal T}_{s,\Omega}$
and ${\mathcal T}_s$ in ${\mathcal G}(\Omega)$, $\OK$, ${\mathcal G}_s(\Omega)$
and $\OK_s$, respectively. The topology ${\mathcal T}_{\Omega}$ induces
${\mathcal T}$, ${\mathcal T}_{s,\Omega}$ and ${\mathcal T}_s$.
The topologies ${\mathcal T}_{s,\Omega}$ and ${\mathcal T}_s$
coincide with the Scarpalezos sharp topologies.