Every Hausdorff Compactification of a Locally Compact Separable Space Is a Ga Compactification

1. I n t r o d u c t i o n . In [4], De Groot and Aarts constructed Hausdorff compactifications of topological spaces to obtain a new intrinsic characterization of complete regularity. These compactifications were called GA compactifications in [5] and [7]. A characterization of complete regularity was earlier given by Fr ink [3], by means of Wallman compactifications, a method which led to the intriguing problem of whether every Hausdorff compactification is a Wal lman compactification. An analogous question was posed by A. B. Paalman de Miranda ; can every Hausdorff compactification of a Tychonoff space be obtained as a G A compactification? We will give a partial answer to this question, suggesting t ha t the answer will be yes. This paper is organized as follows: in the second section we will recall the définition of G A compactifications and we will characterize the class of GA compactifications of a given topological space. Using an analogous characterization of Wallman compactifications, given by Steiner [11], it then follows t ha t every Wallman compactification is a G A compactification. In the third section we will show tha t every Hausdorff compactification of a locally compact separable space is a GA compactification. In fact we have a more general result from which this is a corollary.