During the mid nineteen sixties,
C. E. Aull presented a series of papers in which he distinguished several
different types of paracompact subsets. Using these concepts, three classes
of filter bases are introduced and their convergence and other properties
are studied. A variety of characterizations of paracompactness based on
the existence of certain types of these filter bases and z-filters are given. A
paracompactification construction involving the addition of limit points for one of
the classes of filter bases is presented in detail. Finally, properties of the
paracompactification are explored with some attention given to its ring of continuous
functions.
