Аннотация:An ultrafilter p on ω is said to be discrete if, given any function f:ω→X to any completely regular Hausdorff space, there is an A∈p such that f(A) is discrete. Basic properties of discrete ultrafilters are studied. Three intermediate classes of spaces R1⊂R2⊂R3 between the class of F-spaces and the class of van~Douwen's βω-spaces are introduced. It is proved that no product of infinite compact R2-spaces is homogeneous; moreover, under the assumption d=c, no product of βω-spaces is homogeneous.
