Properties of one-sided ideals of topological rings

A continuous ring isomorphism $\nu\colon(R,\tau)\to(\widehat{R},\widehat{\tau})$ is said to be semitopological from the left (right) in the class $\mathfrak R$ provided $(R,\tau)$ is a left ideal (right ideal, ideal) of a topological ring $(\widetilde{R},\widetilde{\tau})\in\mathfrak R$ and $\nu=\widetilde{\nu}|_R$ for a topological homomorphism $\widetilde{\nu}\colon(\widetilde{R},\widetilde{\tau})\to(\widehat{R},\widehat{\tau})$. The article contains several criteria for a continuous homomorphism to be semi-topological from the left (right).