@MISC{TIETZE_2.MIZ,
  AUTHOR = {P\k{a}k, Karol},
  TITLE = {Tietze Extension Theorem for $n$-dimensional Spaces},
  NOTE = {The paper has been financed by the
    resources of the Polish National Science Centre granted by decision
    no DEC-2012/07/N/ST6/02147.},
  SECTION1 = {Closed Hypercube},
  SECTION2 = {Properties of the Product of Closed Hypercube},
  SECTION3 = {Tietze Extension Theorem},
  DAY = {11},
  MONTH = {February},
  YEAR = {2014},
  ADDRESS1 = {Institute of Informatics\\University of Bia{\l}ystok\\Sosnowa 64, 15-887 Bia{\l}ystok\\Poland},
  SUMMARY = {In this article we prove the Tietze extension theorem for an
             arbitrary convex compact subset of ${\cal E}^n$ with a non-empty
	     interior. This theorem states that, if $T$ is a normal topological
             space, $X$ is a closed subset of $T$, and $A$ is a convex compact
             subset of ${\cal E}^n$ with a non-empty interior, then a
             continuous function $f:X \rightarrow A$ can be extended to a
             continuous function $g:T\rightarrow {\cal E}^n$. Additionally we
             show that a subset $A$ is replaceable by an arbitrary subset of a
             topological space that is homeomorphic with a convex compact
             subset of ${\cal E}^n$ with a non-empty interior. This article
             is based on \cite{DUDA:BM61}; \cite{Engelking:1989},
             \cite{Engelking:1978} can also serve as reference books.}}

@BOOK{Engelking:1989,
       AUTHOR = {Engelking, Ryszard},
        TITLE = {General Topology},
    PUBLISHER = {Heldermann Verlag},
         YEAR = {1989},
      ADDRESS = {Berlin}}

@BOOK{Engelking:1978,
       AUTHOR = {Engelking, Ryszard},
        TITLE = {Dimension Theory},
    PUBLISHER = {North-Holland},
         YEAR = {1978},
      ADDRESS = {Amsterdam}}


