For such spaces the Alexandroff extension is called the one-point compactification or Alexandroff compactification. Source: Internet
In this case it is called the one-point compactification or Alexandroff compactification of X. Recall from the above discussion that any compactification with one point remainder is necessarily (isomorphic to) the Alexandroff compactification. Source: Internet
Descriptive set theory, measure theory and analysis In 1916, Alexandroff and Hausdorff independently solved P. Alexandroff: Sur la puissance des ensembles mesurables B. Comptes rendus Acad. Source: Internet
In particular, homeomorphic spaces have isomorphic Alexandroff extensions. Source: Internet
The one-point compactification In particular, the Alexandroff extension is a compactification of X if and only if X is Hausdorff, noncompact and locally compact. Source: Internet
The theorem of Alexandroff and Hausdorff was a strong impetus for further development of descriptive set theory. Source: Internet