Description:
<jats:title>Abstract</jats:title><jats:p>We extend the comprehensive treatment of<jats:italic>k</jats:italic>-spaces and sequential spaces provided by Franklin's refined notion of a natural cover to<jats:italic>k</jats:italic><jats:sub><jats:italic>R</jats:italic></jats:sub>-spaces and<jats:italic>s</jats:italic><jats:sub><jats:italic>R</jats:italic></jats:sub>-spaces. For this purpose, an apparently unstudied class of maps of topological spaces, the class of<jats:italic>R</jats:italic>-quotient maps, is introduced.</jats:p>