A nonstandard characterization of realcompactness (Q1175926)

Using certain methods from linear programming, the author of this paper presents an interesting and very simple characterization of realcompactness using the language of nonstandard analysis within an enlargement. In particular, a completely regular (Hausdorff) space \(X\) is realcompact if and only if the prenearstandard members of any hyperfinite \(A \subset^* X\) such that \(\text{st}_ X (A) = X\) are also nearstandard. As usual, the operator \(\text{st}_ X\) is the standard part operator.