Inverse Sequences and Absolute Co-Extensors

Volume 55 / 2007

Ivan Ivanšić, Leonard R. Rubin Bulletin Polish Acad. Sci. Math. 55 (2007), 243-259 MSC: 54C55, 54B35, 54F45. DOI: 10.4064/ba55-3-6

Abstract

Suppose that $K$ is a CW-complex, $\mathbf{X}$ is an inverse sequence of stratifiable spaces, and $X=\lim\mathbf{X}$. Using the concept of semi-sequence, we provide a necessary and sufficient condition for $X$ to be an absolute co-extensor for $K$ in terms of the inverse sequence $\mathbf{X}$ and without recourse to any specific properties of its limit. To say that $X$ is an absolute co-extensor for $K$ is the same as saying that $K$ is an absolute extensor for $X$, i.e., that each map $f:A\to K$ from a closed subset $A$ of $X$ extends to a map $F:X\to K$. In case $K$ is a polyhedron $|K|_{\rm CW}$ (the set $|K|$ with the weak topology $\rm CW$), we determine a similar characterization that takes into account the simplicial structure of $K$.

Authors

  • Ivan IvanšićDepartment of Mathematics
    University of Zagreb
    Unska 3
    P.O. Box 148, 10001 Zagreb, Croatia
    e-mail
  • Leonard R. RubinDepartment of Mathematics
    University of Oklahoma
    Norman, OK 73019, U.S.A.
    e-mail

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