@MISC{PSCOMP_1.MIZ,
  AUTHOR = {Byli\'nski, Czes{\l}aw and Rudnicki, Piotr},
  TITLE = {Bounding Boxes for Compact Sets in ${\calE}^2$},
  SECTION1 = {Preliminaries},
  SECTION2 = {Functions into Reals},
  SECTION3 = {Real maps},
  SECTION4 = {Pseudocompact spaces},
  SECTION5 = {Bounding boxes for compact sets in ${\calE}^2$},
  DAY = {29},
  MONTH = {July},
  YEAR = {1997},
  ADDRESS1 = {Warsaw University\\Bia{\l}ystok},
  ADDRESS2 = {University of Alberta\\Edmonton},
  SUMMARY = {We define pseudocompact topological spaces and prove
   that every compact space is pseudocompact. We also solve an
   exercise from \cite{mgm}~p.225 that for a topological space $X$
   the following are equivalent:
   \begin{itemize}
   \item  Every continuous real map from $X$ is bounded (i.e. $X$ 
   is pseudocompact).
   \item  Every continuous real map from $X$ attains minimum.
   \item  Every continuous real map from $X$ attains maximum.
   \end{itemize}
   Finally, for a compact set in $E^2$ we define its bounding rectangle and
   introduce a collection of notions associated with the box.}}

