2022/05/24 by Groznova, Anastasiya, Sipacheva, Ol'ga
#54A35 #54B10 #FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.2205.11978
An ultrafilter p on ω is said to be discrete if, given any function f\colon 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 \mathscr R1 ⊂ \mathscr R2 ⊂ \mathscr 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 \mathscr R2-spaces is homogeneous; moreover, under the assumption \mathfrak d =\mathfrak c, no product of βω-spaces is homogeneous.