We provide a new generalization of realcompactness based on ultrafilters of cozero sets and contrast it with almost realcompactness.
@article{119253, author = {John J. Schommer and Mary Anne Swardson}, title = {Almost$^*$ realcompactness}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {42}, year = {2001}, pages = {385-394}, zbl = {1053.54032}, mrnumber = {1832157}, language = {en}, url = {http://dml.mathdoc.fr/item/119253} }
Schommer, John J.; Swardson, Mary Anne. Almost$^*$ realcompactness. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 385-394. http://gdmltest.u-ga.fr/item/119253/
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