ABSTRACT
This chapter offers a new proof of (a generalization of) I. Juhasz’ theorem that a realcompact space in which each point is an intersection of non-measurably many open sets is of non-measurable cardinality. The context is (for cardinal numbers α≥ω) the α-compact spaces of Herrlich; our principal tool is the concept, introduced in this chapter, of an α-perfect function. At the suggestion of Professor C. E. Aull, the chapter includes a list and a brief commentary concerning the literature on α-compact spaces and perfect functions. It considers for the most part only Tychonoff spaces, i.e., completely regular, Hausdorff spaces. An infinite cardinal (m) is measurable if there is, on the (discrete) set m, a non-principal ultrafilter with the m-intersection property.
