Strong local properties of function spaces with topology of pointwise convergence
by
Francis Jordan
Georgia Southern University

Let X be a space and C(X) stand for the space of real-valued continuous functions with the topology of pointwise convergence. We consider local properties of C(X) that are related to the preservation of local properties under product. We characterize the spaces X such that the product of C(X) with any countably tight or strongly Frechet space Y is again countably tight or strongly Frechet. Under (CH) we construct an uncountable subset W of the real line such that C(W) is has the above product property with respect to the strongly Frechet property. This space is used to answer a question of Gruenhage. Such sets W are shown to have some strong properties. For example, the product or union of such a set with a gamma-set, as defined by Nagy and Gerlits, is again a gamma-set. The class of sets is also closed under finite products and finite unions.

Date received: February 20, 2006