Abstract. It is shown that the class of compact R -monolithic spaces is countably productive.
IntroductionA basic problem in the theory of pseudoradial (or chain-net) spaces is the behaviour of this class of spaces under the product operation. Recently Juhasz and Szentmiklossy [6] proved that assuming 2m < co2 the product of countably many compact pseudoradial spaces is pseudoradial. In ZFC, it is unknown whether even the product of two compact pseudoradial spaces is pseudoradial. Observe, however, that the productivity of pseudoradiality, in general, can be expected to hold only in the class of compact spaces. For instance, / x l(coi), where / is the unit segment and I(oji) is the one point Lindelofization of a discrete space of cardinality (Oi, is a product of two "very good" pseudoradial spaces (one compact metric and the other radial and Lindelof) that is not pseudoradial.Some positive results have been found for certain classes of spaces. For example, in [5] it is shown that the product of a compact radial space and a compact pseudoradial space is pseudoradial, and in [3] it is shown that the product of two compact pseudoradial spaces, one of which is .R-monolithic, is pseudoradial. Later both of these results have been simultaneously generalized in [4].In this paper we prove that the class of compact .R-monolithic spaces is countably productive. In particular, this result improves an analogous one stated in [1], where it is proved that a countable product of compact biradial spaces is pseudoradial.
