@MISC{COMPL_SP.MIZ,
  AUTHOR = {P\c{a}k, Karol},
  TITLE = {Complete Spaces},
  SECTION1 = {Preliminaries},
  SECTION2 = {Cantor's Theorem on Complete Spaces},
  SECTION3 = {Countable Compact Spaces},
  SECTION4 = {The Main Theorem},
  SECTION5 = {Well Spaces},
  DAY = {12},
  MONTH = {October},
  YEAR = {2007},
  ADDRESS1 = {University of Bia{\l}ystok},
  SUMMARY = {This paper is a continuation of \cite{TBSP_1.ABS}.
     First we introduce some definitions needed to formulate
     Cantor's theorem on complete spaces and show several facts
     about them. Next section contains the proof of Cantor's
     theorem and some properties of complete spaces resulting
     from this theorem. Moreover, we define countable compact
     spaces and prove auxiliary facts about them. We also show
     the important condition that every metric space is compact
     if and only if it is countably compact. Then we can prove
     that every metric space is compact if and only if it is
     complete and totally bounded space. We also introduce the
     definition of a metric space with the well metric. This
     article is based on \cite{ENGEL:1}.}}