Inverse Sequences and Absolute Co-Extensors

Ivan Ivanšić ¹   ; Leonard R. Rubin ²

¹ Department of Mathematics University of Zagreb Unska 3 P.O. Box 148, 10001 Zagreb, Croatia
² Department of Mathematics University of Oklahoma Norman, OK 73019, U.S.A.

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 3, pp. 243-259

Résumé

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 $K$.

Détail

DOI : 10.4064/ba55-3-6

Keywords: suppose cw complex mathbf inverse sequence stratifiable spaces lim mathbf using concept semi sequence provide necessary sufficient condition absolute co extensor terms inverse sequence mathbf without recourse specific properties its limit say absolute co extensor saying absolute extensor each map closed subset extends map polyhedron set weak topology determine similar characterization takes account simplicial structure