Suppose that K is a CW-complex, X is an inverse sequence of stratifiable spaces, and X = limX. 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 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 → K from a closed subset A of X extends to a map F:X → K. In case K is a polyhedron (the set |K| with the weak topology CW), we determine a similar characterization that takes into account the simplicial structure of K.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-3-6,
author = {Ivan Ivan\v si\'c and Leonard R. Rubin},
title = {Inverse Sequences and Absolute Co-Extensors},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {55},
year = {2007},
pages = {243-259},
zbl = {1129.54015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-3-6}
}
Ivan Ivanšić; Leonard R. Rubin. Inverse Sequences and Absolute Co-Extensors. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) pp. 243-259. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-3-6/