Algebra and Topology in the Stone-Čech Compactification
نویسندگان
چکیده
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 Ā = {p ∈ βG ∣∣A ∈ p}, for A ⊆ G. Then these sets are actually clopen, and Ā is really the closure in βG of the set A, regarded as a subset of βG under the aforementioned identification of points in G with principal ultrafilters. The semigroup operation + on G is also extended by the formula
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