@MISC{WAYBEL_0.MIZ,
  AUTHOR = {Bancerek, Grzegorz},
  TITLE = {Directed Sets, Nets, Ideals, Filters, and Maps},
  NOTE = {This work has been partially supported by
   Office of Naval Research Grant N00014-95-1-1336.},
  SECTION1 = {Directed subsets},
  SECTION2 = {Nets},
  SECTION3 = {Lower and upper subsets},
  SECTION4 = {Ideals and filters},
  SECTION5 = {Chains},
  SECTION6 = {Semilattices},
  SECTION7 = {Maps},
  SECTION8 = {Completeness wrt directed sets},
  DAY = {12},
  MONTH = {September},
  YEAR = {1996},
  ADDRESS1 = {Institute of Mathematics\\Polish Academy of Sciences},
  SUMMARY = {Notation and facts necessary to start with
the formalization of continuous lattices according to \cite{CCL}
are introduced.
The article contains among other things, the definition
of directed and filtered subsets of a poset
(see 1.1 in \cite[p.~2]{CCL}),
the definition of nets on the poset
(see 1.2 in \cite[p.~2]{CCL}),
the definition of ideals and filters and
the definition of maps preserving arbitrary and directed sups and
arbitrary and filtered infs
(1.9 also in \cite[p.~4]{CCL}).
The concepts of semilattices, sup-semiletices and poset lattices
(1.8 in \cite[p.~4]{CCL})
are also introduced.
A number of facts concerning the above notion and including remarks 1.4, 
1.5, and
1.10 from \cite[pp.~3--5]{CCL}
is presented.}}

