The paper starts with an example of a domain \(R\), complete in its \({\mathfrak P}\)-adic topology, where \({\mathfrak P}\) is not maximal and the \({\mathfrak P}\)-adic topology is not equivalent to the natural one, but \(R_{\mathfrak P}\) is complete in the \({\mathfrak P}_{\mathfrak P}\)-adic topology. Then, the author states conditions for a commutative domain \(R\), endowed with a Hausdorff \({\mathfrak I}\)-adic topology, to give rise to a local ring \(R_{\mathfrak P}\), \({\mathfrak P}\supset {\mathfrak I}\), not complete with respect to its \({\mathfrak I}_{\mathfrak P}\)-adic topology.