Realcompact space

In mathematics, in the field of topology, a topological space is said to be realcompact if it is completely regular Hausdorff and every point of its Stone–Čech compactification is real (meaning that the quotient field at that point of the ring of real functions is the reals). Realcompact spaces have also been called Q-spaces, saturated spaces, functionally complete spaces, real-complete spaces, replete spaces and Hewitt-Nachbin spaces (named after Edwin Hewitt and Leopoldo Nachbin). Realcompact spaces were introduced by Hewitt (1948).