@MISC{WAYBEL_4.MIZ,
  AUTHOR = {Grabowski, Adam},
  TITLE = {Auxiliary and Approximating Relations},
  NOTE = {This work was partially supported by
   the Office of Naval Research Grant N00014-95-1-1336.},
  SECTION1 = {Auxiliary Relations},
  SECTION2 = {Approximating Relations},
  SECTION3 = {Exercises},
  DAY = {21},
  MONTH = {October},
  YEAR = {1996},
  ADDRESS1 = {Warsaw University\\Bia{\l}ystok},
  SUMMARY = {The aim of this paper is to formalize the second part of
   Chapter I Section 1 (1.9--1.19) in \cite{CCL}. Definitions of Scott's auxiliary and
   approximating relations are introduced in this work. We showed
   that in a meet-continuous lattice, the way-below relation is the
   intersection of all approximating auxiliary relations (proposition (40)
   --- compare 1.13 in \cite[pp.~43--47]{CCL}). By (41) a continuous lattice is a complete
   lattice in which $\ll$ is the smallest approximating auxiliary relation.
   The notions of the strong interpolation property and the interpolation
   property are also introduced.}}

