## Inverse Sequences and Absolute Co-Extensors

### Volume 55 / 2007

#### 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 $K$.