On R-monolithic spaces

The class of R-monolithic spaces is properly contained in the class of pseudoradial spaces and includes all sequential spaces, all LOTS and all compact monolithic spaces. We study various properties of these spaces. For instance, it is shown that Changʹs Conjecture reduces the existence of a compact radial non-R-monolithic space of density not exceeding ℵ1 to the existence of a separable space of the same type. Furthermore, we prove that the existence of a compact ccc R-monolithic non-sequential space is undecidable in ZFC and that the class of compact R-monolithic spaces is countably productive.