@MISC{SIMPLEX1.MIZ,
  AUTHOR = {P\c{a}k, Karol},
  TITLE = {Sperner's Lemma},
  SECTION1 = {Preliminaries},
  SECTION2 = {The Area of an Abstract Simplicial Complex},
  SECTION3 = {The Subdivision of a Simplicial Complex},
  SECTION4 = {The Barycentric Subdivision},
  SECTION5 = {Selected Properties of Simplicial Complexes},
  SECTION6 = {The Main Theorem},
  DAY = {9},
  MONTH = {February},
  YEAR = {2010},
  ADDRESS1 = {University of Bialystok, ul. Akademicka 2, 15-267 Bialystok},
  SUMMARY = {In this article we introduce and prove properties of
  simplicial complexes in real linear spaces which are necessary to formulate Sperner's
  lemma. The lemma states that for a function $f$, which for an arbitrary
  vertex $v$ of the barycentric subdivision $\mathcal{B}$ of simplex $\mathcal{K}$
  assigns some vertex from a face of $\mathcal{K}$ which contains $v$,
  we can find a simplex $S$ of $\mathcal{B}$ which satisfies $f(S)=\mathcal{K}$
  (see \cite{ENGEL:BM61}).}}

@BOOK{DUDA:BM61,
 AUTHOR={Duda, Roman},
 TITLE={Wprowadzenie do topologii},
 PUBLISHER={PWN},
 YEAR=1986}
