Near ultrafilters and compactifications (Q1362890)

The author describes the compactification \(X\) of a uniform space \(X\) in terms of the concept of near ultrafilters. He is motivated by the Stone-Čech compactification. The investigation of near ultrafilters is a natural and useful method for describing \(X\). In the paper conditions are investigated for the semigroup compactification and for the compactification of the space of real numbers with its standard uniform structure. The new construction, based on near ultrafilters, is also a generalization of the Wallman compactification.