Summary: We define intrinsic, natural and metrizable topologies \({\mathcal I}_\Omega\), \({\mathcal I}\), \({\mathcal I}_{s,\Omega}\) and \({\mathcal I}_s\) in \({\mathcal G}(\Omega)\), \(\overline\mathbb{K},{\mathcal G}_s(\Omega)\) and \(\overline\mathbb{K}_s\) respectively. The topology \({\mathcal I}_\Omega\) induces \({\mathcal I}\), \({\mathcal I}_{s,\Omega}\) and \({\mathcal T}_s\). The topologies \({\mathcal I}_{s,\Omega}\) and \({\mathcal I}_s\) coincide with the Scarpalezos sharp topologies.