beta omega as a space of ultrafilters

We show that the Stone-Cech compactification of the countable discrete space can be described as the space of ultrafilters on with a topology called the Stone topology. The space of all ultrafilers on is a compact Hausdorff space with a countable dense subset that is a homeomorphic copy of and is thus a compactification of . In addition, this compactification satisfies a function extension property unique to Stone-Cech compactification. Therefore, we can conclude that the space of ultrafilers...