In this work the
correspondence between T2-compactifications, proximity relations, and families of
maximal round filters is extended to the case of T1-spaces. The major results spell
out bijections between a special class of T1-compactifications, certain proximity
relations on the original space, and certain filterfamilies. Perhaps the most interesting
result is the identification of a class of compactifications between T1 and
T2-compactifications. This class consists of the principal weakly regular minimal
compactifications and includes the Wallman compactification, and also the one-point
compactification of a locally compact space. Moreover, the Wallman compactification
is the largest weakly regular minimal compactification of a T1-space. This improves
the known result that the Wallman compactification is T1, and is larger than any
T2-compactification.
