Transfer of information about $\beta N-N$ via open remainder maps
Eric K. van Douwen · Illinois Journal of Mathematics · 1990
All spaces are completely regular, and Hausdorff of course.We use X* to denote /3X-X, and N, Q and R to denote the nonnegative integers, the rationals and the reals.A map is a continuous function.The Stone extension of a map f: X Y is the function/3X /3Y which extends f; it will be denoted by/3f.We use f*, the remainder map, to denote the restriction/3f X*.Recall from [G1] that f* maps X* into Y* if (and only if) f is perfect (= closed + compact fibers); hence f* maps X* onto Y* if f is a perfect map from X onto Y.The closure operators in X,/3X and X* are denoted by cl, C1 and CI*.We use a similar convention for the interior operators int, Int and Int*.We remind the reader that a space X is realcompact if for each x X* there is a G-subset G of/3X with x G __C_ X*. (This is equivalent to the original definition).Clearly Lindel6f spaces are realcompact.