Refinement Suppose and are two prefilters on , and, for each , there is a , such that . Then we say that is ''' than (or refines) ; likewise, is coarser than (or coarsens) . Refinement is a preorder on the set of prefilters. In fact, if also refines , then and are called equivalent, for they generate the same filter. Thus passage from prefilter to filter is an instance of passing from a preordering to associated partial ordering.
Refinement Suppose and are two prefilters on  and for each  there is a  such that  Then we say that is ''' than (or refines) ; likewise is coarser than (or coarsens)  Refinement is a preorder on the set of prefilters In fact if also refines  then and are called equivalent for they generate the same filter Thus passage from prefilter to filter is an instance of passing from a preordering to associated partial ordering