We prove that every compact space X is a Čech-Stone compactification of a normal subspace of cardinality at most d(X)t(X), and some facts about cardinal invariants of compact spaces.

The countably-compactification of a topological space X is such its extension Y, that Y completely regular and countably-compact space, any closed subset in Y. But this does not always exist. Due to this, the concept saturation appeared, which generalisation countably-compactification: instead condition countably-compactness it necessary infinite has limit point Meanwhile, second remains unchan...

The Stone-Čech compactification of discrete semigroups is a tool of central importance in several areas of mathematics, and has been studied extensively. We think of the Stone-Čech compactification of a discrete abelian semigroup G as the set βG of ultrafilters on G, where the point x ∈ G is identified with the principal ultrafilter {A ⊆ G ∣∣x ∈ A}, and the basic open sets are those of the form...