A CHARACTERIZATION OF COMPACTIFICATIONS OF LOCAL COMPACT HAUSDORFF SPACE

Abstract

It is known that different compactification methods are applied to different spaces. In this paper, it is examined some relations among spaces obtained by being applied different compactification methods (One-point compactification, Stone–Cech compactification, Wallman compactification, Fan–Gottesman compactification) to local compact Hausdorff space and these compactifications are characterized with the inequality αX ≅ wX ≅ X* ≤ ⋯ ≤ βX by the addition of lindelöf conditions to studied space. Moreover, it is found maximum and minimum element of the class of all compactifications of the space. We also give an example to illustrate how to apply mathematical result to an application of compactification in physics.